If a-b =7 and a^2 +b^2 = 85, then find the value of a^3 - b^3
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Answer:a^3-b^3=721
Step-by-step explanation:
Given a-b=7 and a^2+b^2=85
First find ab
(a-b)^2=a^2+b^2-2ab
Putting a^2+b^2=85 and a-b=7
7^2=85-2ab
49-85=-2ab
-36/-2=ab
ab=18
As we know a^3-b^3=(a-b)(a^2+ab+b^2)
Put all the values
a^3-b^3=7×(85+18)
7×103
721
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