Statement -1: If a,b,c are distinct real numbers in H.P, then `a^(n)+c^(n)gt2b^(n)" for all "ninN`. Statement -2: `AMgtGMgtHM`A. Statement -1 is true, Statement -2 is True, Statement -2 is a correct explanation for Statement for Statement -1.B. Statement -1 is true, Statement -2 is True, Statement -2 is not a correct explanation for Statement for Statement -1.C. Statement -1 is true, Statement -2 is False.D. Statement -1 is False, Statement -2 is True.

Statement -1: If a,b,c are distinct real numbers in H.P, then `a^(n)+c

1.	Statement -1: If a,b,c are distinct real numbers in H.P, then `a^(n)+c^(n)gt2b^(n)" for all "ninN`. Statement -2: `AMgtGMgtHM`A. Statement -1 is true, Statement -2 is True, Statement -2 is a correct explanation for Statement for Statement -1.B. Statement -1 is true, Statement -2 is True, Statement -2 is not a correct explanation for Statement for Statement -1.C. Statement -1 is true, Statement -2 is False.D. Statement -1 is False, Statement -2 is True.
Answer» Correct Answer - A If a,b,c are in H.P., then b is the HM of a and c. But, the GM of a and c is `sqrt(ac)`. . . .(i) Using `AMgtGM`, we have `(a^(n)+c^(n))/(2)gtsqrt(a^(n)c^(n))` `rArr" "(a^(n)+c^(n))/(2)gt(ac)^(n//2)` `rArr" "(a^(n)+c^(n))/(2)gtb^(n)` `rArr" "a^(n)+c^(n)gt2b^(n)` Hence, statement -1 and 2 are true statement -2 is a correct explanation for statement -1.

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