The fourth proportional to (a²-a b+b²),(a³+ b³) and (a-b) is equal to

Correct Answer is : a2−b2a²-b²a2−b2

Correct Answer is : a2−b2a²-b²a2−b2

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Ratio and Proportion

Question : 78 of 112

Marks: +1, -0

(a^{2}-a b+b^{2}),(a^{3}+

b^{3})

(a-b)

is equal to

Solution:

Concept:

For three quantities

p

q

r

, the fourth proportional is given by

\frac{q \times r}{p}

Explanation:

Here,

p = a^{2} - ab + b^{2}

q = a^{3} + b^{3}

r = a - b

The fourth proportional is

\frac{(a^{3}+b^{3})(a-b)}{a^{2} - ab + b^{2}}

Factor

a^{3}+b^{3}

(a+b)(a^{2} - ab + b^{2})

The numerator becomes

(a+b)(a^{2} - ab + b^{2})(a-b) = (a^{2} - b^{2})(a^{2} - ab + b^{2})

Cancel the common factor

(a^{2} - ab + b^{2})

to obtain

a^{2} - b^{2}

Answer:

a^{2} - b^{2}

, which corresponds to option B.

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