a minus b equals to 7 a square + b square = 85 find a cube minus b cube
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Answer:
a³-b³= 721
Step-by-step explanation:
Here given information is a-b=7 and a²+b²=85
We concludes,
a= b-7.....................(1)
a²+b²=85.........................(2)
Putting the value of a in equation (2)
(b-7)²+b²= 85
b²+49+14b+b²=85
2b²+14b-36=0
b²+7b-18=0
b²+9b-2b-18=0
b(b+9)-2(b+9)=0
(b-2)(b-9)=0
b=2
and a=9
The value of a=9 and b=2
As we know,
a³-b³=(a-b)(a²+ab+b²)
Putting the values of equation (1) & (2)
=7(85+9x2)
=721
Therefore, a³-b³= 721
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