if x+y+z=4 and x²+y²+z²=10 find the value of xy+yz+zx
Class 9 Maths polynomial
Answers
Answered by
0
Answer:
Given,
x+y+z=4 and x
2
+y
2
+z
2
=50
We know,
(a+b+c)
2
=(a
2
+b
2
+c
2
)+2(ab+bc+ca)
Here,
a=x,b=y,c=−z
Thus,
(x+y−z)
2
=x
2
+y
2
+z
2
+2(xy−yz−xz)
=>4
2
=50+2(xy−yz−xz)
=>
2
16−50
=(xy−yz−xz)
=>(xy−yz−xz)=−17
Answered by
0
Answer:
3
Step-by-step explanation:
Given,
x+y+z=4 and x^2+y^2+z^2 =10
We know,
(a+b+c) ^2 =(a^2+b^2 +c ^2 )+2(ab+bc+ca)
Here,
a=x,b=y,c=−z
Thus,
(x+y+z) ^2 = x^2+y^2+z^2 +2(xy+yz+xz)
=>4 ^2 =10+2(xy+yz+xz)
=> 16−10/2 =(xy+yz+xz)
=> (xy+yz+xz) = 3
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