Question

A+b=10 and ab=4 find a2+b2

Answer 1

GIVEN:

The value of a + b = 10

The value of ab = 4

TO FIND:

The value of a² + b²

SOLUTION:

Squaring on both sides

=> (a + b)² = (10)²

We know that,

(a + b)² = a² + b² + 2ab

(10)² = a² + b² + 2(ab)

Substitute the value of ab

100 = a² + b² + 2(4)

100 = a² + b² + 8

=> a² + b² = 100 - 8

=> a² + b² = 92

Therefore, the value of a² + b² is 92.

Answer 2

Given

a+b=10 & ab=4

To Find

a²+b²

Solution

a+b=10 (Both side squaring)

(a+b)²=(10)²

For your information

$\boxed{\boxed{\sf\red{(a+b)^2=a^2+b^2+2ab}}}$

___________________________

=>a²+b²+2ab=100

=>a²+b²+2×4 =100 (Puttting the value of ab)

=>a²+b²+8=100

=>a²+b²=100-8

=92

___________________________

Hence,the value of a²+b²=92

Additional information

$\boxed{\boxed{\sf\red{(a-b)^2=a^2+b^2-2ab}}}$

$\boxed{\boxed{\sf\red{(a^2-b^2)=(a+b)(a-b)}}}$