Find the value of x- -1-x -x2-24-x-1

The correct option is D 5 Squaring both sides, we get ⇒ 1+x√(x^2+24)=(x+1)^2 ⇒ 1+x√(x^2+24)=x^2+1+2x ⇒ x√(x^2+24)=x^2+2x Again squaring both sides, we get ⇒ ...

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Quadratic Equations

Find the valu...

Question

$F i n d t h e v a l u e o f x : \sqrt{1 + x \sqrt{x^{2} + 24}} = x + 1$

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Solution

The correct option is E
5

Squaring both sides, we get
$\Rightarrow 1 + x \sqrt{x^{2} + 24} = (x + 1)^{2} \Rightarrow 1 + x \sqrt{x^{2} + 24} = x^{2} + 1 + 2 x \Rightarrow x \sqrt{x^{2} + 24} = x^{2} + 2 x$
Again squaring both sides, we get
$\Rightarrow {(\sqrt{x^{2} + 24})}^{2} = {(x + 2)}^{2} \Rightarrow x^{2} + 24 = x^{2} + 4 + 4 x \Rightarrow 20 = 4 x \Rightarrow \frac{20}{4} = x \Rightarrow x = 5$

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Find the value of x:√1+x√x2+24=x+1

The correct option is E 5 Squaring both sides, we get ⇒1+x√x2+24=(x+1)2⇒1+x√x2+24=x2+1+2x⇒x√x2+24=x2+2x Again squaring both sides, we get ⇒(√x2+24)2=(x+2)2⇒x2+24=x2+4+4x⇒20=4x⇒204=x⇒x=5

$F i n d t h e v a l u e o f x : \sqrt{1 + x \sqrt{x^{2} + 24}} = x + 1$