if x=1-root2 fibd the value of x^2+1/x^2
Answers
Step-by-step explanation:
Value of x^2+\frac{1}{x^2}x
2
+
x
2
1
is 6.
Step-by-step explanation:
Given: x=1+\sqrt{2}x=1+
2
To find: x^2+\frac{1}{x^2}x
2
+
x
2
1
x² = ( 1 + √2 )² = 1² + (√2)² + 2 × 1 × √2 = 1 + 2 + 2√2 = 3 + 2√2
\frac{1}{x^2}=\frac{1}{3+2\sqrt{2}}=\frac{1}{3+2\sqrt{2}}\times\frac{3-2\sqrt{2}}{3-2\sqrt{2}}
x
2
1
=
3+2
2
1
=
3+2
2
1
×
3−2
2
3−2
2
=\frac{3-2\sqrt{2}}{3^2-(2\sqrt{2})^2}=\frac{3-2\sqrt{2}}{9-8}=3-2\sqrt{2}=
3
2
−(2
2
)
2
3−2
2
=
9−8
3−2
2
=3−2
2
Now,
x^2+\frac{1}{x^2}=3+2\sqrt{2}+3-2\sqrt{2}=6x
2
+
x
2
1
=3+2
2
+3−2
2
=6
Therefore, Value of x^2+\frac{1}{x^2}x
2
+
x
2
1
is 6
Answer:
4 + 5√2
Step-by-step explanation:
Given that x = 1 - √2,
x² + 1 / x²
= (1 - √2)² + 1 / (1 - √2)²
= 1² + √2² - 2[1][√2] +1 / 1² + √2² - 2[1][√2]
= 1 + 2 - 2√2 + 1 / 1 + 2 - 2√2
= 4 - 2√2 / 3 - 2√2
= 4 - 2√2 / 3 - 2√2 × 3 + 2√2 / 3 + 2√2 [rationalise]
= 4 - 2√2[3 + 2√2] / 3 - 2√2[3 + 2√2]
= 12 + 8√2 - 3√2 - 8 / 9 - 8 [ (a - b)(a + b) = a² - b² ]
= 4 + 5√2 / 1
= 4 + 5√2 [answer]
Hope this helps you!!!