Question

If a + 1/a = 6 and a ≠ 0 ; find : (i) a2 + b2 (ii) a2- 1/a2
Which one is correct and prove it.....​

Answer 1

Answer:

a² + 1/a² = 34

a² - 1/a² = -34 + 2a²

Step-by-step explanation:

I believe your Question was,

If a + 1/a = 6 and a ≠ 0 ; find : (i) a² + 1/a² (ii) a² - 1/a²

(i) We know that,

a + 1/a = 6

then,

(a + 1/a)² = 6²

a² + (2 × a × 1/a) + 1²/a² = 36

a² + 2 + 1/a² = 36

so,

a² + 1/a² = 36 - 2

∴ a² + 1/a² = 34 ----- 1

Now,

for (ii) we can't get a number value, and can only be expressed in terms of a²

From above we know that,

1/a² = 34 - a² ----- 2

also,

a² - 1/a² = a² + 1/a² - 1/a² - 1/a²

so,

a² - 1/a² = (a² + 1/a²) - 2(1/a²)

From eq.1 and eq.2 we get

a² - 1/a² = 34 - 2(34 - a²)

a² - 1/a² = 34 - 68 + 2a²

a² - 1/a² = -34 + 2a²

Hope it helped and you understood it........All the best