Question

plz . this is the last h.w. for me today . i have to sleep and wake up very early in the morning for attending online classes . so plz give me right solution as soon as possible plz friends. .​

Answer 1

Answer:

x=2/5

Step-by-step explanation:

root x-root(1-x)=1

=2 root x -root (1-x)=1

=root x (2-root((1/×)-1))=1

=2-root(1-x/x)=root 1/x

=2=root(1+1-x/x)

=2=root(2-x/x)

=2rootx=root (2-x)

square both sides .....

4x=2-x

5x=2

x=2/5

Answer 2

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

$\bigstar\sf{\:(\sqrt{x})+(\sqrt{x})-(1-\sqrt{x})\:=\:1}$

$\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}$

• Value of x .

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

$\mapsto\sf{\:(\sqrt{x})+(\sqrt{x})-(1-\sqrt{x})\:=\:1} \\ \\ \mapsto\sf{\:(2\sqrt{x})\:=\:1+\:(1-\sqrt{x})} \\ \\ \mapsto\sf{\:(2\sqrt{x})\:=\:(2-\sqrt{x})}$

Squaring both side,

$\mapsto\sf{\:(2\sqrt{x})^2\:=\:(2-\sqrt{x})^2} \\ \\ \mapsto\sf{\:4x\:=\:(4+x-2.2.\sqrt{x}} \\ \\ \mapsto\sf{\:4x\:=\:(4+x-4\sqrt{x}} \\ \\ \mapsto\sf{\:(4x-4-x)\:=\:-4\sqrt{x}} \\ \\ \mapsto\sf{\:(3x-4)\:=\:-4\sqrt{x}}$

Again, Squaring both side,

$\mapsto\sf{\:(3x-4)^2\:=\:(-4\sqrt{x})^2} \\ \\ \mapsto\sf{\:(9x^2+16-24x)\:=\:16x} \\ \\ \mapsto\sf{\:(9x^2-24x-16x+16)\:=\:0} \\ \\ \mapsto\sf{\:9x^2-40x+16)\:=\:0} \\ \\ \mapsto\sf{\:(9x^2-40x+16)\:=\:0}$

$\large{\underline{\underline{\mathfrak{\bf{\pink{\:Using\:Dharacharya\:Formula}}}}}}$

$\small\boxed{\sf{\green{\:x\:=\:\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}}$

where,

• a = 9
• b = -40
• c = 16

Keep all values ,

$\mapsto\sf{\:x\:=\:\dfrac{-(-40)\pm\sqrt{(-40)^2-4.9.16}}{2.9}} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{40\pm\sqrt{1600-576}}{18}} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{40\pm\sqrt{1024}}{18}} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{40\pm 32}{18}}$

Take, first (+ ve ) Sign,

$\mapsto\sf{\:x\:=\:\dfrac{40+32}{18}} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{\cancel{72}}{\cancel{18}}} \\ \\ \mapsto\sf{\pink{\:x\:=\:4}}$

Again, Take (- ve) Sign,

$\mapsto\sf{\:x\:=\:\dfrac{40-32}{18}} \\ \\ \mapsto\sf{\:x\:=\:\dfrac{12}{18}} \\ \\ \mapsto\sf{\pink{\:x\:=\:\dfrac{2}{3}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Thus}}}}}$

• Value of x = 4

Or,

• Value of x = 2/3