Question

9.
Given that 5a - 3b = 16 and ab= 15, find the value of
25a2 + 9b2​

Answer 1

Answer:

(5a -3b)^2=16^2

$( {x - y})^{2} = {x}^{2} + {y}^{2} - 2xy$

(5a)^2+ (3b)^2 -2*5a*3b=256

25a^2+9b^2-2(15)=256(adding value of ab)

25a^2+9b^2-30=256

25a^2+9b^2=256-30

25a^2+9b^2=226

Answer 2

We'll use the identity (a^2+b^2)= (a+b)(a^2-ab+b^2).

so, (5a)^2+(3b)^2= (5a+3b)(25a^2-15+9b^2).

=125a^3-75a+45ab^2+75a^2b-45b+27b^3.

Hope it helps..