15. If a3 + b3 = 35, a + b = 5 then ab
(A) 6 (B) 7 (C) 8 (D) 9
Answers
Answer:
Thus the value of a + b is 5
To find:
Value of a + b = ?
Solution:
Given : a3+b3=35a^3 + b^3 = 35a
3
+b
3
=35 and ab=6ab = 6ab=6
Let us take the value of (a+b)=x(a+b)=x(a+b)=x
We know that the value of
(a+b)3=a3+b3+3ab(a+b)( a + b ) ^ { 3 } = a ^ { 3 } + b ^ { 3 } + 3 a b ( a + b )(a+b)
3
=a
3
+b
3
+3ab(a+b)
Substituting (a + b) = x in the above expression, we get,
(x)3=a3+b3+3ab(x)( x ) ^ { 3 } = a ^ { 3 } + b ^ { 3 } + 3 a b ( x )(x)
3
=a
3
+b
3
+3ab(x)
Substituting the value of ab=6ab = 6ab=6 and a3+b3=35a^3 + b^3 = 35a
3
+b
3
=35 in the above derived expression
x3=35+3×6(x)x3=35+18xx3−18x=35x(x2−18)=35x(x2−18)=5×7\begin{lgathered}\begin{array} { c } { x ^ { 3 } = 35 + 3 \times 6 ( x ) } \\\\ { x ^ { 3 } = 35 + 18 x } \\\\ { x ^ { 3 } - 18 x = 35 } \\\\ { x \left( x ^ { 2 } - 18 \right) = 35 } \\\\ { x \left( x ^ { 2 } - 18 \right) = 5 \times 7 } \end{array}\end{lgathered}
x
3
=35+3×6(x)
x
3
=35+18x
x
3
−18x=35
x(x
2
−18)=35
x(x
2
−18)=5×7
Let us take
x=5x=5x=5
And
x2−18=7x2=7+18x2=25x=5\begin{lgathered}\begin{array} { c } { x ^ { 2 } - 18 = 7 } \\\\ { x ^ { 2 } = 7 + 18 } \\\\ { x ^ { 2 } = 25 } \\\\ { x = 5 } \end{array}\end{lgathered}
x
2
−18=7
x
2
=7+18
x
2
=25
x=5
Thus, the value of x is 5.
x=a+b=5x=a+b=5x=a+b=5
Thus, the value of a + b is equal to 5
Answer:
I'm pretty sure its (A)