If a, b, c are in G.P.,then | vedclass

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(B) If $a, b, c$ are in $G.P.$,then $b^2 = ac$.Consider the expression $a(b^2 + c^2) = ab^2 + ac^2$.Since $b^2 = ac$,we can substitute $b^2$ with $ac$

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$a(b^2 + c^2) = c(a^2 + b^2)$

Vedclass · Answer

(B) If $a, b, c$ are in $G.P.$,then $b^2 = ac$.Consider the expression $a(b^2 + c^2) = ab^2 + ac^2$.Since $b^2 = ac$,we can substitute $b^2$ with $ac$:$a(ac) + ac^2 = a^2c + ac^2 = c(a^2 + ac)$.Alternatively,starting from $b^2 = ac$:$b^2(a - c) = ac(a - c)$$b^2a - b^2c = a^2c - ac^2$$b^2a + ac^2 = a^2c + b^2c$$a(b^2 + c^2) = c(a^2 + b^2)$.Verification: Let $a = 1, b = 2, c = 4$.$LHS = a(b^2 + c^2) = 1(4 + 16) = 20$.$RHS = c(a^2 + b^2) = 4(1 + 4) = 4(5) = 20$.Since $LHS = RHS$,option $B$ is correct.

If $a, b, c$ are in $G.P.$,then

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