Question

X + Y = 13 equal root x + root y

Answer 1

Pls fast solve this question

Answer 2

Proved that X + Y = 13 is equal root x + root y which is 13

Given:  

X + Y = 13 equal root x + root y

To prove:

$\sqrt{x}+\sqrt{y}=13$

Solution:  

As X + Y = 13, we can say that

Y = 13 - X ---------- (1)

$\sqrt{x}+\sqrt{y}=13\\\sqrt{x}+\sqrt{x}-13=13$ (As per equation 1)

Squaring on both the sides,

$\begin{array}{c}{x+(x-13)+2 \sqrt{x}(x-13)=169} \\ {x+x-13+2 \sqrt{x}(x-13)=169} \\ {2 x-182=-2 \sqrt{x}(x-13)} \\ {x-91=\sqrt{x}(x-13)}\end{array}$

Squaring on both the sides,

$\begin{array}{l}{(\mathrm{x}-91)^{2}=\mathrm{x}^{2}-13 \mathrm{x}} \\ {\mathrm{x}^{2}+(91)^{2}-182 \mathrm{x}=\mathrm{x}^{2}-13 \mathrm{x}} \\ {169 \mathrm{x}=91 \times 91}\end{array}$

$\begin{array}{l}{\mathrm{x}=\frac{91 \times 91}{169}} \\ {\mathrm{X}=\frac{91 \times 91}{13 \times 13}} \\ {\mathrm{x}=7 \times 7=49}\end{array}$

Now, Y = 13 - X  

= 13 - 49

= -36.

Therefore, x + y = 49 + (-36) = 13  

and  root x + root y = $\sqrt{49}+\sqrt{-36}$ = 7 + 6 = 13

Hence, proved.