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Question

(A) Given the expression: $(\sqrt{5}+3)^{2} = a+b\sqrt{5}$.Using the algebraic identity $(x+y)^{2} = x^{2} + 2xy + y^{2}$,where $x = \sqrt{5}$ and $y

Vedclass · Accepted Answer

$a=14, b=6$

Vedclass · Answer

(A) Given the expression: $(\sqrt{5}+3)^{2} = a+b\sqrt{5}$.Using the algebraic identity $(x+y)^{2} = x^{2} + 2xy + y^{2}$,where $x = \sqrt{5}$ and $y = 3$:$(\sqrt{5})^{2} + 2(\sqrt{5})(3) + (3)^{2} = a+b\sqrt{5}$.$5 + 6\sqrt{5} + 9 = a+b\sqrt{5}$.$14 + 6\sqrt{5} = a+b\sqrt{5}$.By comparing the rational and irrational parts on both sides,we get $a = 14$ and $b = 6$.

For each question,select the proper option from four options given,to make the statement true: If $(\sqrt{5}+3)^{2}=a+b \sqrt{5}$,then........

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