a-b = 7 and ab = 2 , find a^3 - b^3
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ANSWER
Given,
a+b=7 and ab=15
Squaring both sides,we get,
(a+b)
2
=7
2
=a
2
+b
2
+2ab=49 [since(a+b)
2
=a
2
+b
2
+2ab]
=a
2
+b
2
+2(15)=49
=a
2
+b
2
=49−30
=a
2
+b
2
=19
Now,
(a
3
+b
3
)
=(a+b)(a
2
+b
2
−ab)
=7(19−15)
=7(4)
=28
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