Question

if 2ab + 5cd=5 and abcd=1,what is the value of 4a2b2 + 25c2d2?​

Answer 1

Answer:

Staring with your given values of:

2ab + 5cd = 5 and abcd = 1

Let's start with squaring both sides of the first equation:

(2ab + 5cd)² = 5²

4a²b² + 20abcd + 25c²d² = 25

Since abcd = 1, make the substitution and simplify:

4a²b² + 20(1) + 25c²d² = 25

4a²b² + 20 + 25c²d² = 25

Subtract 20 from both sides:

4a²b² + 25c²d² = 5

And there is your expression that you are being asked to solve for, equal to 5.