Question

if x+y+z=10 and x 2 +y 2 +z 2 =40,find xy+yz+zx

Answer 1

(x+y+z)²=x²+y²+z²+2(xy+yz+zx)
10²=40+2(xy+yz+zx)
2(xy+yz+zx)=100-40=60
xy+yz+zx=30

Hope you find this answer helpful.

Answer 2

Answer:

$xy+yz+zx= 30$

Step-by-step explanation:

$Given \: x+y+z=10--(1)\\x^{2}+y^{2}+z^{2}=40---(2)$

/* On Squaring both sides of equation (1) , we get

$(x+y+z)^{2}=(10)^{2}$

$\implies x^{2}+y^{2}+z^{2}+2xy+2yz+2zx=100$

$\implies 40+2(xy+yz+zx)=100$

$\implies 2(xy+yz+zx)=100-40$

$\implies 2(xy+yz+zx)=60$

$\implies xy+yz+zx= \frac{60}{2}$

$\implies xy+yz+zx= 30$

Therefore,

$xy+yz+zx= 30$

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