Question

solve for x: (x-5)^2 - (x-2)^2 = -2​

Answer 1

SOLVE THE EQUATION :-

${(x - 5)}^{2} - {(x - 2)}^{2} = - 2 \\ \\ \\ \implies {x}^{2} + {5}^{2} - 2 \times x \times 5 - ( {x}^{2} + {2}^{2} - 2 \times x \times 2) = - 2 \\ \\ \\ \implies {x}^{2} + 25 - 10x - ( {x}^{2} + 4 - 4x) = - 2 \\ \\ \\ \implies {x}^{2} + 25 - 10x - {x}^{2} - 4 + 4x = - 2 \\ \\ \\ \implies 21 - 6x = - 2 \\ \\ \\ \implies - 6x = - 23 \\ \\ \\ \implies \boxed{x = \frac{23}{6} = 3 \frac{5}{6} }$

Answer 2

The correct answer is "x = 23/6".

Step-by-step explanation:

$The \ given \ expression \ is:\\\\(x-5)^2-(x-2)^2=-2\\\\On \ applying \ formula \ "(a-b)^2=a^2+b^2-2ab",we \ get\\\\(x^2+25-10x)-(x^2+4-4x)=-2\\\\x^2+25-10x-x^2-4+4x=-2\\\\21-6x=-2\\\\On \ adding \ "6x" \ both \ sides,we \ get\\\\21-6x+6x=-2+6x\\\\21=-2+6x\\\\On \ adding \ "2" \ both \ sides,we \ get\\\\21+2=-2+6x+2\\\\23=6x\\\\x=\frac{23}{6}$

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