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Question Number 187473 by Rupesh123 last updated on 17/Feb/23

Answered by HeferH last updated on 17/Feb/23

Commented by HeferH last updated on 17/Feb/23

 (√((5(√2))^2 −1)) = 7   5a + b = 7  5b + a = 5    a = (5/4); b = (3/4)   ⇒ ((x + 3)/4) = (4/(x − 3))   x = 5    ⇒ A_△  = (((x +1)(7+x))/2) =((6∙12)/2) = 36u^2

$$\:\sqrt{\left(\mathrm{5}\sqrt{\mathrm{2}}\right)^{\mathrm{2}} −\mathrm{1}}\:=\:\mathrm{7}\: \\ $$$$\mathrm{5}{a}\:+\:{b}\:=\:\mathrm{7} \\ $$$$\mathrm{5}{b}\:+\:{a}\:=\:\mathrm{5}\: \\ $$$$\:{a}\:=\:\frac{\mathrm{5}}{\mathrm{4}};\:{b}\:=\:\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\:\Rightarrow\:\frac{{x}\:+\:\mathrm{3}}{\mathrm{4}}\:=\:\frac{\mathrm{4}}{{x}\:−\:\mathrm{3}} \\ $$$$\:{x}\:=\:\mathrm{5}\: \\ $$$$\:\Rightarrow\:{A}_{\bigtriangleup} \:=\:\frac{\left({x}\:+\mathrm{1}\right)\left(\mathrm{7}+{x}\right)}{\mathrm{2}}\:=\frac{\mathrm{6}\centerdot\mathrm{12}}{\mathrm{2}}\:=\:\mathrm{36}{u}^{\mathrm{2}} \\ $$

Commented by Rupesh123 last updated on 18/Feb/23

Excellent!

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