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प्रश्न
If a + b = 11 and a2 + b2 = 65; find a3 + b3.
उत्तर
a + b = 11 and a2 + b2 = 65
Now, (a+b)2 = a2 + b2 + 2ab
⇒ (11)2 = 65 + 2ab
⇒ 121 = 65 + 2ab
⇒ 2ab = 56
⇒ ab = 28
a3 + b3 = ( a + b )( a2 - ab + b2)
= (11)(65 - 28)
= 11 x 37
= 407
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