Question

15. If 3x + 5y = 11 and xy = 2, find the value of: 9x2 + 25y2

Answer 1

The problem provides the information:

3 x + 5 y = 11

and x y = 2

Asking to find the value of 9 x^2 + 25 y^2

so we proceed to recall what the square of a binimial of the following form is:

`(3x+5y)^2=(3x)^2+2(3x\cdot5y)+(5y)^2=9x^2+30xy+25y^2_{}`

So, we see that the square of the quantity: (3 x + 5 y) which from the information given equals 11^2 = 121, must equal the expression:

9 x^2 + 25 y^2 + 30 x y.

then we write the following equation making both parts equal:

`\begin{gathered} 11^2=9x^2+25y^2+30xy \\ 121=9x^2+25y^2+30xy \\ 121=9x^2+25y^2+30(2) \\ 121-60=9x^2+25y^2 \\ 61=9x^2+25y^2 \end{gathered}`

Therefore the value of 9 x^2 + 25 y^2 = 61