practice problems

 Q1.


2) Solve:

xy + x + y = 23 
yz + y + z = 31 
zx + z + x = 47

Add 1 on both sides
(x+1)(y+1) = 24 = XY
(z+1)(y+1) = 32 = ZY
(x+1)(z+1) = 48 = XZ

Multiply all and take square root
(XYZ)^2 = 24.32.48 = 6.4.8.4.8.6 => XYZ = -+4.6.8
XYZ/XY = Z = -+8
Similarly Y = -+4, X = -+6

Q3
Solve:
3x(x + y − 2) = 2y 
y(x + y − 1) = 9x

Let x + y - 1 = p and y/x = q assuming x !=0 
Upon solving you will get 2 solutions:
p = -2,3 = x + y - 1=> q = -9/2,3 = y/x

Solving further you will get
x = 1, y = 3 and x = 2/7, y = -9/7

Earlier we assumed x !=

Q4.

Solve for x:
2p(p − 2)x = (p − 2)

S4.
p != 2 => x = 1/2p and p !=0
p = 2 => it is true for infinitely many values of x


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