Question

If a2 + b2=99 , ab=9, find the value of a-b ​

Answer 1

Answer:

a 2+b 2 =99 ab=9

(a−b)2 = =a 2 +b 2-9ab

=99-9(9)

=99-81

a-b =18

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Answer 2

The value of a - b is 9.

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Let's understand a few concepts:

To find the value of a - b we will use the following algebraic formula:

$\bigstar \:\boxed{\bold{(a - b)^2 = a^2 - 2ab + b^2}}\:\bigstar$

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Let's solve the given problem:

Here we have,

a² + b² = 99

ab = 9

We will now use the above-mentioned algebraic formula,

(a - b)²

= a² - 2ab + b²

= (a² + b²) - (2 × ab)

= (99) - (2 × 9)

= 99 - 18

= 81

∴ (a - b)² = 81

• taking square roots on both sides

⇒ √(a - b)² = √81

⇒ a - b = 9

Thus, the value of a - b = 9.

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