If a, b, c are in A. P., a 2 , b 2 , c 2 are in H.

Question

If a, b, c are in A. P., a2, b2, c2 are in H. P. , then prove that either a = b = c or a, b, -c/2 form a G. P.

Aditi Chauhan · Accepted Answer

Hello Student,Please find the answer to your questionGiven that a, b, c are in A. P.&rArr; 2b = a + c &hellip;&hellip;. (1)And a2, b2, c2 are in H. P.&rArr;&rArr; (a &ndash; b)(a + b)/b2a2 = (b &ndash; c) (b + c)/b2c2&rArr; ac2 + bc2 = a2b + a2c [∵ a &ndash; b = b &ndash; c]&rArr; ac (c &ndash; a) + b (c &ndash; a) (c + a) = 0&rArr; (c &ndash; a) (ab + bc + ca) = 0&rArr; either c &ndash; a = 0 or ab + bc + ca = 0&rArr; either c = a or (a+ c) b + ca = 0 and then form (i) 2b2 + ca = 0Either a = b = c or b2 = a (-c/2)i.e. a, b, -c/2 are in G. P. Hence ProvedThanksAditi ChauhanaskIITians Faculty

Algebra> If a, b, c are in A. P., a 2 , b 2 , c 2 ...

If a, b, c are in A. P., a2, b2, c2 are in H. P. , then prove that either a = b = c or a, b, -c/2 form a G. P.

Simran Bhatia , 10 Years ago

Aditi Chauhan

Swayam

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Algebra> If a, b, c are in A. P., a 2 , b 2 , c 2 ...

If a, b, c are in A. P., a2, b2, c2 are in H. P. , then prove that either a = b = c or a, b, -c/2 form a G. P.

Simran Bhatia , 10 Years ago

Aditi Chauhan

Swayam

Provide a better Answer & Earn Cool Goodies

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Ask a Doubt

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