Question

If 25a ^ 4 + 20a ^ 2 * b ^ 2 + 16b ^ 4 = 75 and 5a ^ 2 + 4b ^ 2 - 2sqrt(5) * a * b = 15 , what is the value of ab?

Answer 1

Answer:

25a

2

−4b

2

−28bc−49c

2

=(5a)

2

−(2b)

2

+28bc−(7c)

2

=(5a)

2

−{(2b)

2

+2×2b×7c−(7c)

2

}

∵[(a+b)

2

=a

2

+b

2

+2ab]

=(5a)

2

−(2b+7c)

2

∵[a

2

−b

2

=(a−b)(a+b)]

={(5a)−(2b+7c)}{(5a)+(2b+7c)}

=(5a−2b−7c)(5a+2b+7c)