Question

if a+1/a=3 find value of a2+1/a2

Answer 1

Given

$\to \sf \left( a + \dfrac{1}{a} \right) = 3$

To find the value of

$\to \sf \left( a ^{2} + \dfrac{1}{a^{2} } \right)$

Now Take

$\to \sf \left( a + \dfrac{1}{a} \right) = 3$

Using Squaring on both side

$\to \sf \left( a + \dfrac{1}{a} \right) ^{2} = (3) ^{2}$

$\to \sf \left( a {}^{2} + \dfrac{1}{a {}^{2} } + 2 \times x \times \dfrac{1}{x} \right) = 9$

$\to \sf \left( a {}^{2} + \dfrac{1}{a {}^{2} } + 2\right) = 9$

$\to \sf \left( a {}^{2} + \dfrac{1}{a {}^{2} }\right) = 9 - 2$

$\to \sf \left( a {}^{2} + \dfrac{1}{a {}^{2} }\right) = 7$

Answer

$\to \sf \left( a {}^{2} + \dfrac{1}{a {}^{2} }\right) = 7$

Answer 2

Step-by-step explanation:

Given:-

$\sf a+ \dfrac{1}{a}=3$

To find:-

$\sf a^2+\dfrac{1}{a^2}$

Solution:-

$\rm \longmapsto a + \frac{1}{a} = 3 \\ \sf \: by \: taking \: square \\ \rm \longmapsto (a + \frac{1}{a} ) {}^{2} = {3}^{2} \\ \sf \: we \: know \: that \\ \boxed{ {(a + b)}^{2} = a {}^{2} + 2ab + {b}^{2} } \\ \rm \longmapsto {a}^{2} + 2 \times a \times \frac{1}{a} +( { \frac{1}{a}) }^{2} = 9 \\ \rm \longmapsto {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 9 \\ \rm \longmapsto {a}^{2} + \frac{1}{ {a}^{2} } = 9 - 2 \\ \rm \longmapsto {a}^{2} + \frac{1}{ {a}^{2} } = 7$