Algebra — Page 1 — Tinkutara Math Forum

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Question 229471

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Question 229367

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∫(1/( ((ax^n +bx^(n−1) +cx^(n−2) +dx^(n−3) ...+φx^1 +μ))^(1/n) ))dx idk . you can try.i was just feeling bored

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{ ((2^x ∙ 4^y^2 = 256)),((lnx + + 2lny = ln(lg100000000))) :} ⇒ x+y=?

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a_n =((a_(n−2) .a_(n−1) )/(2a_(n−2) −a_(n−1) )) a_1 =1; a_2 =(3/7); a_(2019) =(p/q) p and q are relatively prime numbers p−q=?

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Σ_(r=1) ^∞ (r^3 /(r!))=?

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Question 228756

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Question 228720

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Given ((a + b(√(cx))))^(1/3) + ((a − b(√(cx))))^(1/3) = d Determine x in terms of a, b, c and d. Solution: Let A = ((a + b(√(cx))))^(1/3) and B = ((a − b(√(cx))))^(1/3) ⇒ A^3 = a + b(√(cx)) and B^3 = a − b(√(cx)) ⇒ A^3 + B^3 = 2a ⇒ (A + B)[(A + B)^2 − 3AB)] = 2a ⇒ d(d^2 − 3AB) = 2a ⇒ AB = ((d^3 − 2a)/(3d)) ((a + b(√(cx))))^(1/3) × ((a − b(√(cx))))^(1/3) = ((d^3 − 2a)/(3d)) a^2 − b^2 cx = (((d^3 − 2a)^3 )/(27d^3 )) x = (a^2 /(b^2 c)) − (((d^3 − 2a)^3 )/(27b^2 cd^3 ))

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inversion of question 228499 find one cubic y=ax^3 +bx^2 +cx+d with 3 real zeros which touches these 3 parabolas: y=−5x^2 y=−(1/7)x^2 y=(2/3)x^2 (it′s possible!)

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Question 228499

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a,b,c,d ∈ R a(1−a) + b(3−b) + c(5−c) + d(7−d) Find: max(a,b,c,d) = ?

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Question 228451

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Question 228417

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Question 228414

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Find: lim_(x→(𝛑/2)) [(x − (π/2)) tanx] = ?

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Two cars travel from point A to point B, a distance of 200km. Car X travels at an average speed of 60km/h with a tyre radius of 20cm, while Car Y travels at an average speed of 50km/h with a tyre radius of 25cm. Assuming all other conditions are identical, which car arrives at point B first? (a) car X (b) car Y (c) both arrive at the same time (d) cannot be determined

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Quartic: x^4 +ax^3 +bx^2 +cx+d=0 (x^2 +px+h)(x^2 +qx+k)=0 p+q=a h+k=b−pq=b−m (pq=m say) pk+qh=c hk=d q(h+k)=q(b−m) p(h+k)=p(b−m) ph+qk=c k(p−q)=p(b−m)−c h(p−q)=c−q(b−m) multiplying d(a^2 −4m)= ac(b−m)−m(b−m)^2 −c^2 m(b−m)^2 +(ac−4d)m +a(ad−bc)+c^2 =0 −−−−−−−−−−−−−−− m^3 −2bm^2 +(b^2 +ac−4d)m +a(ad−bc)+c^2 =0 −−−−−−−−−−−−−−− p , q=(a/2)±(√((a^2 /4)−m)) −−−−−−−−−−−−−−− h=((c−q(b−m))/(p−q)) k=((p(b−m)−c)/(p−q)) −−−−−−−−−−−−−−− x=−(p/2)±(√((p^2 /4)−{((c−q(b−m))/(p−q))})) or −−−−−−−−−−−−−− x=−(q/2)±(√((q^2 /4)−{((p(b−m)−c)/(p−q))})) −−−−−−−−−−−−−−−

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{ ((a + 2b + 5c + 3d = 1146)),((2a + 3b + 2c + d + 3e = 1279)),((5a + b + 2c + d + 3e = 1555)),((4a + 2b + 3c + d + e = 1459)),((a + 2b + 2c + 2d + 4e = 1194)) :} Find: (a;b;c;d;e) = ?