If x - 1-x - 5 find the value of x-2 - 1-x-2 - Maths Q-A

Compute the required value.It is given that, x+1/x=5.On squaring both sides, we get;(x+1/x)^2=250ex0ex⇒x^2+1/x^2+2=250ex0ex⇒x^2+1/x^2=23 [Since, (a+b)^2=a^2+b ...

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Standard VII

Mathematics

Equal Angles Subtend Equal Sides

If x + 1/x = ...

Question

If $x + \frac{1}{x} = 5$ , find the value of $x^{2} + \frac{1}{x^{2}}$ .

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Solution

Compute the required value.
It is given that, $x + \frac{1}{x} = 5$ .
On squaring both sides, we get;
${(x + \frac{1}{x})}^{2} = 25 \Rightarrow x^{2} + \frac{1}{x^{2}} + 2 = 25 \Rightarrow x^{2} + \frac{1}{x^{2}} = 23$ [Since, ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$ ]
Therefore, the value of $x^{2} + \frac{1}{x^{2}}$ is $23$ .

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If x+1x=5, find the value of x2+1x2.

Compute the required value.It is given that, x+1x=5.On squaring both sides, we get;x+1x2=25⇒x2+1x2+2=25⇒x2+1x2=23 [Since, (a+b)2=a2+b2+2ab]Therefore, the value of x2+1x2 is 23.

If $x + \frac{1}{x} = 5$ , find the value of $x^{2} + \frac{1}{x^{2}}$ .