Assertion -If a- b- c are three positive numbers in G-P- then a - b - c-3 - c - b-ab - bc - ca - -abc 2 Reason- A-M- H-M- - G-M-2 is true for any set of positive numbers-

The correct option is C Assertion is correct but Reason is incorrectAssertion : #160; (AM)(HM) = (GM^2)^2 True for any 3 numbers in G.P ...

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Byju's Answer

Standard XII

Mathematics

Continuity of a Function

Assertion :If...

Question

Assertion :If a, b, c are three positive numbers in G.P., then $(\frac{a + b + c}{3}) . (\frac{c + b}{a b + b c + c a}) = {(\sqrt[3]{a b c})}^{2}$ Reason: (A.M.) (H.M.) = $(G . M .)^{2}$ is true for any set of positive numbers.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is C Assertion is correct but Reason is incorrect
Assertion : $(A M) (H M) =$ $(G M^{2})^{2}$
True for any $3$ numbers in $G . P .$
Reason : False if number are not in $G . P .$

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Assertion :If a, b, c are three positive numbers in G.P., then (a+b+c3).(c+bab+bc+ca)=(3√abc)2 Reason: (A.M.) (H.M.) = (G.M.)2 is true for any set of positive numbers.

The correct option is C Assertion is correct but Reason is incorrectAssertion : (AM)(HM)= (GM2)2True for any 3 numbers in G.P.Reason : False if number are not in G.P.

Assertion :If a, b, c are three positive numbers in G.P., then $(\frac{a + b + c}{3}) . (\frac{c + b}{a b + b c + c a}) = {(\sqrt[3]{a b c})}^{2}$ Reason: (A.M.) (H.M.) = $(G . M .)^{2}$ is true for any set of positive numbers.

The correct option is C Assertion is correct but Reason is incorrect
Assertion : $(A M) (H M) =$ $(G M^{2})^{2}$
True for any $3$ numbers in $G . P .$
Reason : False if number are not in $G . P .$