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4-2.Quadratic Equations and Inequations
hard
સમીકરણ $x^2+|2 x-3|-4=0$, ના તમામ બીજ ના વર્ગોનો સરવાળો _______ છે.
A$3(3-\sqrt{2})$
B$6(3-\sqrt{2})$
C$6(2-\sqrt{2})$
D$3(2-\sqrt{2})$
(JEE MAIN-2025)
Solution
$ x ^2+|2 x -3|-4=0$
$\text { Case I: } x \geq \frac{3}{2}$
$ x ^2+2 x -3-4=0$
$x^2+2 x-7=0$
$x=2 \sqrt{2}-1$
$\text { Case II }: x<\frac{3}{2}$
$x^2+3-2 x-4=0$
$x^2-2 x-1=0$
$x=1-\sqrt{2}$
$\text { Sum of squares }=(2 \sqrt{2}-1)^2+(1-\sqrt{2})^2$
$= 8-4 \sqrt{2}+1+1-2 \sqrt{2}+2$
$= 6(2-\sqrt{2}) \therefore(3)$
$\text { Case I: } x \geq \frac{3}{2}$
$ x ^2+2 x -3-4=0$
$x^2+2 x-7=0$
$x=2 \sqrt{2}-1$
$\text { Case II }: x<\frac{3}{2}$
$x^2+3-2 x-4=0$
$x^2-2 x-1=0$
$x=1-\sqrt{2}$
$\text { Sum of squares }=(2 \sqrt{2}-1)^2+(1-\sqrt{2})^2$
$= 8-4 \sqrt{2}+1+1-2 \sqrt{2}+2$
$= 6(2-\sqrt{2}) \therefore(3)$
Standard 11
Mathematics
