If x
2
+y
2
+z
2
=xy+yz+zx, then the value of (
8x
2
y
2
+6y
2
z
2
+10z
2
x
2
17x
4
+9y
4
+16z
4
) is:
- A2
- B3.25
- C2.5
- D1.75
Solution & Step-by-step Explanation
The condition x
2
+y
2
+z
2
=xy+yz+zx is satisfied if and only if x=y=z.
Let x=y=z=1.
Substitute these values into the given expression:
8(1)
2
(1)
2
+6(1)
2
(1)
2
+10(1)
2
(1)
2
17(1)
4
+9(1)
4
+16(1)
4
=
8+6+10
17+9+16
=
24
42
=
4
7
=1.75
2
+y
2
+z
2
=xy+yz+zx is satisfied if and only if x=y=z.
Let x=y=z=1.
Substitute these values into the given expression:
8(1)
2
(1)
2
+6(1)
2
(1)
2
+10(1)
2
(1)
2
17(1)
4
+9(1)
4
+16(1)
4
=
8+6+10
17+9+16
=
24
42
=
4
7
=1.75