If the sum and the product of two numbers are 8 and 15 respectively, find the sum of
their cubes.
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If the sum and the product of two numbers are 8 and 15 respectively, find the sum of
their cubes.
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Let the two numbers be x and y
According to the first condition
x+y=8
x=8-y ...(i)
According to the second condition
xy=15
(8-y)y=15 .....(From i)
8y-y^2=15
y^2-8y+15=0
y^2-5y-3y+15=0
y (y-5)-3 (y-5)=0
(y-3)(y-5)=0
y=3,5
Substituting the value of y in equation (i) We get
x=8-3=5 or x=8-5=3
Now, Sum of their cubes
3^3+5^3
=27+125
=152
The x,y combination is either x=3 and y=5 or x=5 and y=3 regardless of the combination,the sum of their cubes is 152