If x + y + z = 19, x2 + y2 + z2 = 133, and xz = y2, x > z > 0, what is the value of (x - z)?
A. 0
B. 5
C. -2
D. -5
Answer: Option B
Solution(By Examveda Team)
x + y + z = 19, x2 + y2 + z2 = 133 and xz = y2(x - z) = ?
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
361 = 133 + 2(xy + yz + y2)
228 = 2(x + y + z)y
$$y = \frac{{114}}{{19}} = 6$$
x + z = 13
xz = 36
x - z = ?
(x + z)2 - (x - z)2 = 4xz
169 - (x - z)2 = 144
x - z = 5
Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
Join The Discussion