Question

the sum of squares of 3 numbers is 170 whike the sum of their products taken to at a time is 157.What is the sum of the numbers​

Answer 1

Answer:

x + y + z = 22

Explanation:

$x {}^{2} + y {}^{2} + z {}^{2} = 170 \\ xy + yz + xz = 157$

(a + b + c)^2 = a^2 + b^2 +c^2 +2ab+2bc+2ac

a^2 + b^2 +c^2 = (a + b+ c)^2-2ab-2bc-2ac

We know that,

x^2 + y^2 + z^2 = 170

(x + y + z)^2 - 2xy -2yz -2xz = 170

(x + y + z)^2 - 2 [ xy + yz + xz ] = 170

(x + y + z)^2 - 2 [157] = 170

(x + y + z)^2 = 170 + 2 [157] = 170 + 314 =484

(x + y + z) = $\sqrt{484} = 22$

---------------

Hope it helps....!

■♤♤■