if x+y+z=8,xy+yz+zx=20, find x²+y²+z²
Answers
Answered by
18
-32 is the correct answer!
property used ==>
(x+y+z)² = x²+y²+z²+2(xy+yz+zx)
hope it helps you friend!
Answered by
32
Answer:
Hence, the value of x^2 + y^2 + z^2 is 24.
Step-by-step explanation:
Given:-
x + y + z = 8
and
xy + yz + zx = 20
To find out:-
Value of x^2 + y^2 + z^2
Solution:-
We have,
x + y + z = 8
Squaring on both sides, we get
→ (x + y + z)^2 = (8)^2
→ x^2 + y^2 + z^2 + 2xy + 2yz + 2zx = 64
→ x^2 + y^2 + z^2 + 2(xy + yz + zx) = 64
→ x^2 + y^2 + z^2 + 2(20) = 64
[ ∵ xy + yz + zx = 20]
→ x^2 + y^2 + z^2 + 40 = 64
→ x^2 + y^2 + z^2 = 64 - 40
→ x^2 + y^2 + z^2 = 24
Answer:-
Hence, the value of x^2 + y^2 + z^2 is 24.
:)
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