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If a, b, c are in A.P., then a^2+4b^3 + c^3 is equal to ______

Question

If $a, b, c$ are in A.P., then $a^{2} + 4 b^{3} + c^{3}$ is equal to ______.

3 b (a^{2} + c^{2})

3 b (a^{2} - c^{2})

3 b (c^{2} - a^{2})

3 b^{2} (a^{2} + c^{2})

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Oliver Discussed

a, b, c

are in A.P., then

a^{2} + 4 b^{3} + c^{3}

is equal to ______.

12 mins ago

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12 mins ago

Text solutionVerified

a, b, c

are in A.P., then

a^{3} + 4 b^{3} + c^{3} = a^{3} + 4 (\frac{a + c}{2})^{3} + c^{3}

= a^{3} + c^{3} + \frac{1}{2} (a + c)^{3}

= \frac{3}{2} (a^{3} + c^{3} + a^{2} c + a c^{2})

= 3 (\frac{a + c}{2}) (a^{2} + c^{2})

= 3 b (a^{2} + c^{2})

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Question Text	If $a, b, c$ are in A.P., then $a^{2} + 4 b^{3} + c^{3}$ is equal to ______.
Answer Type	Text solution:1
Upvotes	150