If the roots of the equation (a^2 + b^2)x^2 - | vedclass

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(B) The given equation is $(a^2 + b^2)x^2 - 2b(a + c)x + (b^2 + c^2) = 0$.Expanding the middle term: $(a^2 + b^2)x^2 - 2(ab + bc)x + (b^2 + c^2) = 0$.

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Geometric Progression

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(B) The given equation is $(a^2 + b^2)x^2 - 2b(a + c)x + (b^2 + c^2) = 0$.Expanding the middle term: $(a^2 + b^2)x^2 - 2(ab + bc)x + (b^2 + c^2) = 0$.Rearranging the terms: $(a^2x^2 - 2abx + b^2) + (b^2x^2 - 2bcx + c^2) = 0$.This simplifies to: $(ax - b)^2 + (bx - c)^2 = 0$.Since the sum of squares is zero,each term must be zero: $ax - b = 0$ and $bx - c = 0$.Thus,$x = \frac{b}{a}$ and $x = \frac{c}{b}$.Equating the values of $x$: $\frac{b}{a} = \frac{c}{b}$.This implies $b^2 = ac$,which means $a, b, c$ are in Geometric Progression.

If the roots of the equation $(a^2 + b^2)x^2 - 2b(a + c)x + (b^2 + c^2) = 0$ are equal,then in which progression are $a, b, c$?

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