Fourth proportional to (a2 - b2), (a2 - ab), (a3 + b3) is
A. a - b
B. a4 + b4
C. a(a2 - ab + b2)
D. a3 - a2b2 + b2
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let the fourth proportional to}} \cr & \left( {{a^2} - {b^2}} \right),\left( {{a^2} - ab} \right),\left( {{a^3} + {b^3}} \right)\,{\text{be}}\,x \cr & {\text{Then,}} \cr & = \left( {{a^2} - {b^2}} \right):\left( {{a^2} - ab} \right)::\left( {{a^3} + {b^3}} \right):x \cr & \Rightarrow \left( {{a^2} - {b^2}} \right)x = \left( {{a^3} + {b^3}} \right)\left( {{a^2} - ab} \right) \cr & \Rightarrow x = \frac{{\left( {{a^3} + {b^3}} \right)\left( {{a^2} - ab} \right)}}{{\left( {{a^2} - {b^2}} \right)}} \cr & \Rightarrow x = \frac{{\left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)a\left( {a - b} \right)}}{{\left( {a - b} \right)\left( {a + b} \right)}} \cr & \Rightarrow x = a\left( {{a^2} - ab + b} \right) \cr} $$Related Questions on Ratio
If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to
A. 2 : 1
B. 14 : 3
C. 7 : 2
D. 1 : 2
If $$\frac{2}{3}$$ of A=75% of B = 0.6 of C, then A : B : C is
A. 2 : 3 : 3
B. 3 : 4 : 5
C. 4 : 5 : 6
D. 9 : 8 : 10
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