Question

What is the value of ab if (a+b)²=36 (a-b)²=24?

Answer 1

Answer: ab=3

Step-by-step eexplanation:-

(a+b)^2 = a^2 + b^2 + 2ab = 36 -------- eq. 1

(a-b)^2 = a^2 + b^2 - 2ab = 24 -------- eq. 2

Adding the 2 equations...

60 = 2a^2 + 2b^2

Dividing the equation by 2...

30 = a^2 + b^2 -------- eq. 3

Now, substitute eq. 3 in eq. 1

30 + 2ab = 36

2ab = 6

ab = 3

I hope it was helpful..

Answer 2

Explanation :

(a + b) ^ 2 + (a - b) ^ 2 = 36 + 24 a ^ 2 + b ^ 2 + 2ab + a ^ 2 - 2ab + b 60

2(a ^ 2 + b ^ 2) = 6b

a ^ 2 + b ^ 2 = 60/2

x ^ 2 + b ^ 2 = 3a ^ 2

=

Now given (a + b) ^ 2 = 3

a ^ 2 + b ^ 2 + 2ab = 36 3a + 2ab = 36

2ab = 36 - 30

zab = 6

iab = 6/2

ab >= 3