Question

If √ax-√by=b-a and √bx-√ay=0 then find the value of x and y.​

Answer 1

Answer:

$x = - \sqrt{a } & y = - \sqrt{b}$

Answer 2

$\Large{\underbrace{\sf{\orange{Required\:Answer:}}}}$

The given equation are:-

√ax-√by=b-a -------------------------------(i)

√bx-√ay=0 --------------------------------(2)

Put √a= p and √b= q in given equation, we get:-

Px- qy= q²-p² ---------------------------------(3)

qx - py=0 ---------------------------------(4)

Adding eq.(3) & (4) we get:-

Px+ qx - qy -py = q² - p²

⟹x(p+q) -y(p+q)=q² - p²

⟹(p+q)•(x - y) = q² - p²

⟹(x - y)= -(p²-q²)/p+q

⟹(x - y)=$\displaystyle{\bf{ \dfrac{-(p+q)•(p-q)}{p+q}}}$

⟹(x - y)=-(p-q)

⟹(x - y)=-p+q. ----------------------------(5)

Subtracting (4) from (3) we get:-

Px-qx-qy+py = q²-p²

⟹x(p-q)+y(p-q)=q²-p²

⟹(p-q)•(X+y) =q²-p²

⟹(x+y)= -(p²-q²)/p-q

⟹(x +y)=$\displaystyle{\bf{ \dfrac{-(p+q)•(p-q)}{p-q}}}$

⟹(x +y)=-(p+q)

⟹(x +y)=-p - q. ----------------------------(6)

Addinging (5) and (6) we get:-

➜2x= - 2p

➜x = -p

➜ x = -√a. [ as p= √a]

Subtracting (5) from (6) we get:-

➜2y= -2p

➜y = -p

➜y = -√b. [ as q= √b]

Hence, x = -√a. and y = -√b.