(C) Given equation is $3^{x^2-x} = 25 - 4^{x^2-x}$.Rearranging the terms,we get $4^{x^2-x} + 3^{x^2-x} = 25$.We know that $25 = 16 + 9 = 4^2 + 3^2$.So

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(C) Given equation is $3^{x^2-x} = 25 - 4^{x^2-x}$.Rearranging the terms,we get $4^{x^2-x} + 3^{x^2-x} = 25$.We know that $25 = 16 + 9 = 4^2 + 3^2$.So,the equation becomes $4^{x^2-x} + 3^{x^2-x} = 4^2 + 3^2$.Comparing the powers,we get $x^2 - x = 2$.This simplifies to the quadratic equation $x^2 - x - 2 = 0$.Factoring the quadratic,we get $(x - 2)(x + 1) = 0$.Thus,the solutions are $x = 2$ and $x = -1$.Therefore,option $C$ is correct.

Class 11 Mathematics 2 Complex Numbers and Quadratic Equations: Quadratic Equations Solution of quadratic equations and Nature of roots

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Solve the equation,$3^{x^2-x}=25-4^{x^2-x}$

AP EAMCET 2020 All AP EAMCET

A
$-1$ only
B
$2$ only
C
Both $-1$ and $2$
D
No solution

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2 Complex Numbers and Quadratic Equations: Quadratic Equations

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Solve the equation,$3^{x^2-x}=25-4^{x^2-x}$

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