If for a non-zero x, 7x
2
+5x+7=0, then x
3
+
x
3
1
is ________.
- A610
343
- B343
420
- C420
610
- D343
610
Solution & Step-by-step Explanation
Given:
7x
2
+5x+7=0
Divide the entire equation by 7x:
x+
7
5
+
x
1
=0⟹x+
x
1
=−
7
5
We need to find x
3
+
x
3
1
:
x
3
+
x
3
1
=(x+
x
1
)
3
−3(x+
x
1
)
=(−
7
5
)
3
−3(−
7
5
)
=−
343
125
+
7
15
=
343
−125+15×49
=
343
−125+735
=
343
610
7x
2
+5x+7=0
Divide the entire equation by 7x:
x+
7
5
+
x
1
=0⟹x+
x
1
=−
7
5
We need to find x
3
+
x
3
1
:
x
3
+
x
3
1
=(x+
x
1
)
3
−3(x+
x
1
)
=(−
7
5
)
3
−3(−
7
5
)
=−
343
125
+
7
15
=
343
−125+15×49
=
343
−125+735
=
343
610