How can we solve if 2x +3y=13 and xy=6 find the value of 8x³+27y³. This math problem I got as my assignment, so how to answer if 2x +3y=13 and xy=6 find the value of 8x³+27y³?

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## dynamicapps5

The value of 8x³+27y³ is 1729. When the given problem is If 2x +3y=13 and xy=6 find the value of 8x³+27y³.

Given

2x+3y = 13 and xy = 6

and we need 8x³+27y³

We know

(a+b)³ = a² + b² + 3ab(a+b) apply this rule to (2x+3y) = 13

(2x+3y) ³ = (13)³

(2x)³ + (3y)³ + 2x*3y (2x+3y) = 2197

8x³+27y³ + 6xy (2x+3y) = 2197

Sub xy = 6 and 2x+3y=13 in

above Equation.

8x³ +27y³ + 6(6) (13) = 2197

8x³+27y³+ (36) (13) = 2197

8x³+27y³ = 2197-468

8x³ +27y³ = 1729.

Refer below image for clear solution.

You may also go go through this math problem with written answer if x2+y2=10xy then prove-that 2log(x +y )= logx+ logy+ 3log2