Question

Solve the value of (a-b)^2 given that a^2+b^2=15 and ab=3.

Answer 1

• (a - b)² = 9

Explanation:

Given

• a² + b² = 15,
• ab = 3.

Find

• Value of (a - b)²

Solution

Use identity:

• (a - b)² = a² - 2ab + b²

Substitute values:

• (a - b)² = a² + b² - 2ab = 15 - 2*3 = 15 - 6 = 9

Answer 2

(a - b)² = 9

Explanation:

Expand (a - b)²:

`\begin{aligned}\implies (a-b)^2&=a^2-2ab+b^2\\&=a^2+b^2-2ab\end{aligned}`

Given:

• a² + b² = 15
• ab = 3

Substitute the given values into the expanded equation:

`\begin{aligned}\implies (a-b)^2&=a^2+b^2-2ab\\&=15-2(3)\\&=15-6\\&=9\end{aligned}`

Therefore, (a - b)² = 9.