If x=7−4
3
, then find the value of (x
2
+
x
2
1
).
- A197
- B196
- C194
- D195
Solution & Step-by-step Explanation
Given:
x=7−4
3
Let's find
x
1
by rationalizing the denominator:
x
1
=
7−4
3
1
×
7+4
3
7+4
3
=
7
2
−(4
3
)
2
7+4
3
=
49−48
7+4
3
=7+4
3
Now, add x and
x
1
:
x+
x
1
=(7−4
3
)+(7+4
3
)=14
Squaring both sides:
(x+
x
1
)
2
=14
2
x
2
+
x
2
1
+2=196
x
2
+
x
2
1
=196−2=194
x=7−4
3
Let's find
x
1
by rationalizing the denominator:
x
1
=
7−4
3
1
×
7+4
3
7+4
3
=
7
2
−(4
3
)
2
7+4
3
=
49−48
7+4
3
=7+4
3
Now, add x and
x
1
:
x+
x
1
=(7−4
3
)+(7+4
3
)=14
Squaring both sides:
(x+
x
1
)
2
=14
2
x
2
+
x
2
1
+2=196
x
2
+
x
2
1
=196−2=194