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If a+b =11 and a²+b²=65 then what is the value of a³+b³?!????!

If a+b =11 and a²+b²=65 then what is the value of a³+b³?!????!

Grade:9

2 Answers

Manish
13 Points
6 years ago
If a+b = 11 and,a²+b²=65 so ,(a+b)² = a²+b²+2ab , Put 11 in a+b and 65 in a²+b² to get ab(11)²= 65 + 2ab121 = 65 + 2ab2ab = 56ab = 28Put the value of ab in :a³+b³ = (a+b)³ - 3ab( a+b) = (11)³ - 3×28(11) = 1331 - 924 = 407
Soumendu Majumdar
159 Points
5 years ago
Dear Student,
 
(a+b)^2 = a^2 + b^2 + 2ab
Put (a+b) = 11 & a^2 + b^2 = 65
so
11^2= 65 + 2ab
implies   2 ab = 56
so       ab =28
Now,
a^3 + b^3 = (a+b)(a^2 -ab + b^2) = (11)(65 - 28) = 11 x 37 =  407 (Ans)
Hope it helps!

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