468,564 views
13 votes
13 votes
Solve the value of (a-b)^2 given that a^2+b^2=15 and ab=3.

User Laudarch
by
3.2k points

2 Answers

14 votes
14 votes

Answer:

  • (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
User Ndrizza
by
2.8k points
15 votes
15 votes

Answer:

(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.

User Memphis Meng
by
3.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.