Question

if 3 X + 5 Y is equal to 11 and X Y is equal to 2 find the value of 9 X square + 25 y square

Answer 1

(3x+5y)^2= 9x^2+25y^2+2×3x×5y
(11)^2= 9x^2+25y^2+30xy
121= 9x^2+25y^2+30×2xy
121= 9x^2+25y^2+60
-9x^2+25y^2= -121+60
-9x^2+25y^2= -61
9x^2+25y^2= 61

Answer 2

3x+5y=11
xy=2
Squaring the equation 3x+5y and then using Identity (a+b)²=a²+b²+2ab
(3x+5y)²=(3x)²+(5y)²+2×3x×5y
Putting the values
(11)²=9x²+25y²+30(2)
121=9x²+25y²+60
121- 60 = 9x²+25y²
9x²+25y²=61