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Let `a, x, b` in A.P, `a, y, b` in GP `a, z, b` in HP where `a` and `b` are disnict positive real numbers. If `x = y + 2` and `a = 5z`, then which of the following is/are `COR RECT` ?A. `y^(2) = zx`B. `x gt y gt z`C. `a = 9 , b = 1`D. `a = (1)/(4), b = -(9)/(4)` |
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Answer» Correct Answer - A::B::C `{:(a_(1)x_(1)b,"inA.P.",rArr,2x=a+b),(a_(1)y_(1)b,"inG.P.",rArr,y^(2)=ab),(a_(1)z_(1)b,"inA.P.",,):}` `rArr z = (2ab)/(a + b)` `:. x gt y gt z (A gt G gt H)` at `y^(2) = xz` `:. a = 5z` , (Given)…….(i) `(a)/(5) = (2ab)/(a + b)` or `a = 9b` `x = y + 2` or `(a + b)/(2) = sqrt(ab) + 2` or `5b = 3b + 2 , (b gt 0)` `:. (1,2,3)` |
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