If \: \: a + (1)/(a) = 3 \: prove \: that \: {a}^(2) \frac{1}{ {a}^(2) } = 7 .................​....

Question

`If \: \: a + (1)/(a) = 3 \: prove \: that \: {a}^(2) \frac{1}{ {a}^(2) } = 7`

.................​....

Answer 1

a+1/a = 3 -----(1)

a²+1/a² = 7

By doing square of equation 1

(a+1/a)² = 9

a²+1/a²+ 2 ×a × 1/a = 9 using (a+b)²=a²+b²+2ab

a²+1/a²+2=9

a² + 1/a² = 9-2

a²+1/a²= 7 Ans.