Q31. यदि [(x2 + y2 + z2 – 64) / (xy – yz – zx)] = -2 हो तथा (x + y) = 3z हो, तो z = ?
[(x2 + y2 + z2 – 64) / (xy – yz – zx)] = -2
(x2 + y2 + z2 – 64) = -2(xy – yz – zx)
(x2 + y2 + z2 – 64) = -2xy + 2yz + 2zx
(x2 + y2 + 2xy) + z2 – 64 = 2z(y + x)
(x + y)2 + z2 – 64 = 2z(y + x) {∵ (x + y) = 3z दिया है}
(3z)2 + z2 – 64 = 2z(3z)
9z2 + z2 – 64 = 6z2
4z2 = 64
z = 4
Q32. [1/(1×4) + 1/(4×7) + 1/(7×10) + 1/(10×13) + 1/(13×16)] = ?
= (1/3){[1 – 1/4] + [1/4 – 1/7] + [1/7 – 1/10] + [1/10 – 1/13] + [1/13 – 1/16]}
= (1/3){[1 – 1/16]}
= (1/3)[15/16]
= 5/16
