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