If a-1-a - 5-then find the value of a2-1-a2-

Given, a+1/a = 5 Using the identity, (a+b)^2=a^2+2ab+b^2 we get, (a+1/a)^2 = a^2+2 nbsp;× a nbsp;× nbsp;1/a + (1/a)^2 ⇒ (5)^2 = nbsp; a^2+2+ 1/a^2 ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic identity for (a+b)^2

If a+1/a = 5,...

Question

$If (a + \frac{1}{a}) = 5,$
$then find the value of (a^{2} + \frac{1}{a^{2}}) .$

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Solution

The correct option is B 23
$Given, a + \frac{1}{a} = 5$

Using the identity,
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$

we get,
$(a + \frac{1}{a})^{2} = a^{2} + 2 \times a \times \frac{1}{a} + (\frac{1}{a})^{2}$

$\Rightarrow (5)^{2} = a^{2} + 2 + \frac{1}{a^{2}}$

$\Rightarrow a^{2} + \frac{1}{a^{2}} = 25 - 2$

$\Rightarrow a^{2} + \frac{1}{a^{2}} = 23$

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If (a+1a) =5, then find the value of (a2+1a2).

The correct option is B 23Given, a+1a =5 Using the identity, (a+b)2=a2+2ab+b2 we get, (a+1a)2=a2+2×a×1a+(1a)2 ⇒(5)2=a2+2+1a2 ⇒a2+1a2=25−2 ⇒a2+1a2=23

$If (a + \frac{1}{a}) = 5,$
$then find the value of (a^{2} + \frac{1}{a^{2}}) .$