Test Index

Ratio and Proportion

Question : 94 of 112

Marks: +1, -0

\; \frac{a^{3}+3a}{3a^{2}+1} = \; \frac{91}{37}

then 'a' equals

Solution:

Concept:

Solve rational equation by cross‑multiplication, then test the given options.

Explanation:

Given

\frac{a^{3}+3a}{3a^{2}+1} = \frac{91}{37}

Cross‑multiply:

37(a^{3}+3a) = 91(3a^{2}+1)

Expand:

37a^{3} + 111a = 273a^{2} + 91

Bring all terms to one side:

37a^{3} - 273a^{2} + 111a - 91 = 0

Now test each option.

For

a=7

37(343) - 273(49) + 111(7) - 91 = 12691 - 13377 + 777 - 91 = 0

Thus

a=7

satisfies the equation.

No need to test others as the correct option is found.

Answer:

a = 7

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