Question

a2-b2=3, ab=2, find a+b

Answer 1

ANSWER.

• a + b = ±3.

SOLUTION.

Given –

→ a² - b² = 3 – (i)

→ ab = 2 – (ii)

From (ii), we get,

→ b = 2/a

Substituting the value of b in (i), we get,

→ a² - (2/a)² = 3

→ (a⁴ - 4)/a² = 3

→ a⁴ - 4 = 3a²

→ a⁴ - 3a² - 4 = 0

Let u = a²,

→ u² - 3u - 4 = 0

→ u² - 4u + u - 4 = 0

→ u(u - 4) + 1(u - 4) = 0

→ (u + 1)(u - 4) = 0

Substitute back u = a², we get,

→ (a² + 1)(a²- 4) = 0

→ (a² + 1)(a + 2)(a - 2) = 0

Therefore,

→ (a² + 1) = 0 or (a + 2) = 0 or (a - 2) = 0

So,

→ a = √-1, 2, -2

But we omit complex roots.

So, a = ±2

When a = 2,

→ ab = 2

→ 2b = 2

→ b = 1

When a = -2,

→ ab = 2

→ -2b = 2

→ b = -1

So,

→ a + b = 2 + 1, -2 - 1

→ a + b = ±3 (Answer)