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 D
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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Similar questions

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

If $x - \frac{1}{x} = - 1,$ find the value of $x^{2} + \frac{1}{x^{2}}$ .

Q. If

x - \frac{1}{x} = - 1

. Find value of

x^{2} + (\frac{1}{x})^{2}

Q. If

(x - \frac{1}{x}) = 8

, find the value of
(i)

(x + \frac{1}{x})

(ii)

(x^{2} - \frac{1}{x^{2}})

Q. If

x + \frac{1}{x} = 9

and

x^{2} + \frac{1}{x^{2}} = 5

. Find the value of

x - \frac{1}{x}

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Find the value of x:√1+x√x2+24=x+1

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

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