Question

solve :2/√x+3/√y=2;4/√x -9/√y=-1​

Answer 1

Let y=2+3–√

⟹y−1=1y=12+3–√=2−3–√

(2+3–√)x2–2x+1=y(x−1)2

(2−3–√)x2–2x−1=(y−1)x2–2x+1–2=y−(x2–2x+1).y2=y2y(x−1)2

42−3–√=4∗(2+3–√)=4y

(2+3–√)x2–2x+1+(2−3–√)x2–2x−1=42−3–√

⟹y(x−1)2+y2y(x−1)2=4y

Let p=y(x−1)2

⟹p+y2p=4y

⟹p2−4yp+y2=0

p=4y±(4y)2−4(1)(y2)−−−−−−−−−−−−−√2=4y±12y2−−−−√2=2y±3y−−√

⟹p=(2±3–√)y

If p=(2+3–√)y:

⟹p=y.y=y2

⟹p=y(x−1)2=y2

⟹(x−1)2=2

⟹x=1±2–√

If p=(2−3–√)y:

⟹p=1y.y=1

⟹p=y(x−1)2=1=y0

⟹(x−1)2=0

⟹x=1

Ans:

x=1 OR 1±2–√