Question

a
$a4+a2b2+ b4 = 12 \: and \: {a2} +ab + {b2} = 4 \: then \: ab = ?$
​

Answer 1

Step-by-step explanation:

a⁴+a²b²+b⁴ = 12.............(1)

a²+ab+b²= 4

=> a²+b² = 4-ab..............(2)

from(1)

a⁴+a²b²+b⁴ = 12

=>. (a²+b²)²- a²b²= 12

=>. (4-ab)²-a²b² = 12. from(2)

=> 16+a²b²-8ab-a²b² = 12

=> 8ab = 4

=> ab = 1/2

=> b = 1/2a

putting it in the equation (2)

a²+(1/2a)² = 4-1/2

=>. a²+1/4a² = 7/2

=> 4a⁴+1 = 14a²

=> 4a⁴-14a²+1 = 0

you can solve this simple quadratic equation

for the value of a. also by substituting the

value of a you find a.

hope this helps you