Question

If x+y+z=7 and 1/x+1/y+1/z =10/xyz ,then find the value of x^2+y^2+z^2+1

Answer 1

Answer:

Step-by-step explanation:

Given :-

x+y+z=7

$\frac{1}{x} +\frac{1}{y} + \frac{1}{z} = \frac{10}{xyz}$

To find:-

x²+y²+z²+1 = ?

Solution:-

x²+y²+z²+1 = (x+y+z)² - 2(xy+yz+zx)

calculation:-

$\frac{1}{x} +\frac{1}{y} + \frac{1}{z} = \frac{10}{xyz}$

(xy+yz+zx)/xyz = 10xyz

(xy +yz+zx )= 10

According to question

x²+y²+z² = (x+y+z)² - 2(xy+yz+zx)

x²+y²+z² = (x+y+z)² - 2(10)

x²+y²+z² = (7)² - 2(10)

x²+y²+z² = 49-20

x²+y²+z² = 29