Arithmetic — Page 1 — Tinkutara Math Forum

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x = ^3 (√(16)) + ^3 (√(36)) − ^3 (√(24)) ((10)/x^6 ) − (x^3 /(10^3 )) − ((30)/x^3 ) = ?

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Question 228520

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a_(n+2) = a_n + a_(n+1) n≥1 . a_7 = 120 a_8 =?

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Find x = ? => (1/(a+b+x)) = (1/a) + (1/b) + (1/x) = (1/(a+b+x)) −(1/x) = (1/a) + (1/b) = ((x −(a+b+x))/(x(a+b+x))) = ((b+a)/(ab)) = ((x−a−b−x)/(ax+bx+x^2 )) = ((b+a)/(ab)) = ((−a−b )/(x^2 +ax+bx )) = ((b+a)/(ab)) = ((−(a+b) )/(x^2 +ax+bx )) = ((b+a)/(ab)) = ((−1 )/(x^2 +ax+bx )) = (1/(ab)) = −ab = x^2 +ax+bx = 0= x^2 +ax+bx+ab = 0 = x(x+a)+b(x+a) = 0 = (x+a)(x+b) => x+a = 0 => x+b = 0 x = −a x = −b

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A team that is 100 meters long is moving forward in a straight line at a constant speed. A messenger runs at a constant speed from the rear of the team to the front to deliver a message. Then without changing the speed he runs back to the rear of the team. By the time he returns to the rear the team has advanced 240 meters. How far has the messenger traveled?

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Question 227139

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Question 226943

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Question 226942

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Question 226919

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let gcd(m,n)=1. Determine gcd(5^m +7^m ,5^n +7^n )

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By using De Moivres theorm simplify (a)(((cos (π/2)−isin (π/2))(cos (π/3)+isin (π/3)))/(cos (π/3)−isin (π/3))) (b)((cos (π/8)+isin (π/8))/(cos (π/6)+isin (π/6)))

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Prove that (a−b)(a−c)(a−d)(b−c)(b−d)(c−d) divisible by 12

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Question 226721

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Question 226697

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Question 226612

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Question 226609

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Question 226608

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Question 226586

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Question 226585

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Find gcd(a^2 +ab+b^2 ,ab) if gcd(a,b)=1

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Question 226464

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Question 226455

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Question 226177

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(3/7)^0 prove and evalute show all working

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Question 225599

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3k+4=n^2 . k,n ∈N Find all n numbers .

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Same problem with me please fix the problem

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Question 224305

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Calculate I=∫^( +∞) _( 0) [(1/t)−(1/(sh(t)))]^( 2) dt

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demontrer que quelque soit k appartenant N l

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is it possible to prove that mn(m+n)(m−n) divisible by 6 always

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let gcd(n,m)=1. Determine gcd(5^m +7^m ,5^n +7^n )

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Determine gcd(13a+19b,ab) given that gcd(a,19)=gcd(b,13)=1

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proof gcd(2^m −1,2^n −1)=2^(gcd(m,n)) −1

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Question 223125

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Question 222736

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Prove that : (a−b)(a−c)(a−d)(b−c)(b−d)(c−d) divisible by 12, with a,b,c,d ∈Z

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Prove:∀n∈Z^+ ,1^3 +2^3 +…+n^3 =(1+2+…+n)^2

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Question 222097

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(√((1−4x(√(1−4x^2 )))/2)) = 1−8x^2 x=?

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Question 221247

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Question 220738

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Question 220737

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for all x , y [0 , 1] ; prove that; [ (((x^3 + y^3 + 𝛇(3)))^(1/(3 )) /(1 + e^(−x^2 y^2 ) )) + (((x^4 + 𝚪(y+1)))^(1/(4 )) /((1 + y^2 )^(1/3) )) + ((ln(1 + x^5 + y^5 ))/( (√(1 + x^2 + y^2 )))) + Li_2 (xy) + ((√(x^6 + y^6 +1 ))/((1 + x^3 y^3 )^(1/2) )) ≤ (e^(xy) /(1 + x + y )) + ((ln (1 + x^2 + y^2 ) ))^(1/(3 )) + ((2𝛇(2))/( (√(1 + x^2 y^2 )))) + ((x^8 + y^8 + 1))^(1/(4 )) ]

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for all x, y ∈ [0 , 1] ; prove that; (1/( (√(1 + x^4 )))) + (2/( (√(1 + y^4 )))) + (2/( (√(4 + (x + y)^4 )))) + ((2(√2))/( (√(2+ x^2 y^2 + y^3 )))) ≤ (2/( (√(1 + x^2 y^2 )))) + (2/(^4 (√(1 + x^5 + y^5 )))) + ln(e+((x^3 y+y^3 x)/(1 + xy))) + (1/((1+x+y)^3 ))

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let a, b, c, d, e is a positive real numbers and K = a + b + c + d + e +1 . prove that; Σ_(cyc) (1/(k−a)) < (1/4) ((((e^3 d^3 c))^(1/(4 )) /(c^(3/4) d^(1/2) e^(1/4) (√a))) + (((d^( 3) c^2 b))^(1/(4 )) /(d^( 3/4) c^(1/2) b^(1/4) (√e))) + (((c^3 b^2 a))^(1/(4 )) /(c^(3/4) b^(1/2) a^(1/4) (√d))) + (((b^3 a^2 e))^(1/(4 )) /(b^(3/4) a^(1/2) e^(1/4) (√c))) + (((a^3 e^2 d))^(1/(4 )) /(a^(3/4) e^(1/2) d^(1/4) (√b))))