The number of pairs of reals (x, y) such that | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(a)

We have,

$x =x^2+y^2$

$	ext { and } y =2 x y$

$\because y-2 x y =0$

$\Rightarrow y(1-2 x) =0$

$\Rightarrow y=0, x =\frac{1}{2}$

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(a)

We have,

$x =x^2+y^2$

$	ext { and } y =2 x y$

$\because y-2 x y =0$

$\Rightarrow y(1-2 x) =0$

$\Rightarrow y=0, x =\frac{1}{2}$

Put $y=0$ in Eq. (i), we get

$x =x^2+0$

$\Rightarrow x-x^2=0$

$\Rightarrow x(1-x)=0$

$\Rightarrow x=0, x=1$

$	ext { Put } x=\frac{1}{2} 	ext { in Eq. (i), we get }$

${\frac{1}{2}=\left(\frac{1}{2}ight)^2+y^2}$

$\Rightarrow y^2=\frac{1}{2}-\frac{1}{4}$

$\Rightarrow \quad y^2=\frac{1}{4} \Rightarrow y=\pm \frac{1}{2}$

$	herefore 	ext { Value of }(x, y) \operatorname{are}(0,0)(0,1)$

$\left(\frac{1}{2}, \frac{1}{2}ight)\left(\frac{1}{2}, \frac{-1}{2}ight)$

The number of pairs of reals $(x, y)$ such that $x=x^2+y^2$ and $y=2 x y$ is

Similar Questions

Let $y = \sqrt {\frac{{(x + 1)(x - 3)}}{{(x - 2)}}} $, then all real values of $x$ for which $y$ takes real values, are

Suppose the quadratic polynomial $p(x)=a x^2+b x+c$ has positive coefficient $a, b, c$ such that $b-a=c-b$. If $p(x)=0$ has integer roots $\alpha$ and $\beta$ then what could be the possible value of $\alpha+\beta+\alpha \beta$ if $0 \leq \alpha+\beta+\alpha \beta \leq 8$

The number of real solutions of the equation $e ^{4 x }+4 e ^{3 x }-58 e ^{2 x }+4 e ^{ x }+1=0$ is..........

If $x$ is real and $k = \frac{{{x^2} - x + 1}}{{{x^2} + x + 1}},$ then

Let $\alpha, \beta, \gamma$ be the three roots of the equation $x ^3+ bx + c =0$. If $\beta \gamma=1=-\alpha$, then $b^3+2 c^3-3 \alpha^3-6 \beta^3-8 \gamma^3$ is equal to $......$.