If the sum of two numbers is 6 and the sum of their cubes is 126, find the sum of their squares
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Let two number be a and b,
According to question,we get,
a+b=7
a
3
+b
3
=133
Now,
(a+b)
3
=a
3
+b
3
+3ab(a+b)
=>7
3
=133+3ab(7)
=>
21
343−133
=ab
=>ab=
21
210
=>ab=10
Now,
(a+b)
2
=a
2
+b
2
+2ab
=>7
2
=a
2
+b
2
+2(10)
=>a
2
+b
2
=49−20
=>a
2
+b
2
=29
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