if x = ✓3 + ✓2, find x⁴ -1/x⁴
Answers
Answer:
Step-by-step explanation:
value of x⁴ - 4x³ + x² + x - √3 = 2
it is given that, x = 2 + √3
⇒(x - 2) = √3
squaring both sides we get,
⇒(x - 2)² = (√3)²
⇒x² - 4x + 4 = 3
⇒x² - 4x + 1 = 0...….(1)
we have to find value of x⁴ - 4x³ + x² + x - √3
= x²(x² - 4x + 1) + x - √3
from equation (1) we get,
= x² × 0 + x - √3
= 0 + (2 + √3 ) - √3
= 2
hence, x⁴ - 4x³ + x² + x - √3 = 2
also read similar questions : If x = cube root (2 + square root 3), then what is x cube + 1/x cube?
brainly.in/question/4040294
if x= root[ 3+2 root 2] then find the value of x to the power 4+ 1/ x to the power 4
Answer:x+
x
1
=3−2
2
+
3−2
2
1
x
1
=
3−2
2
1
×
3+2
2
3+2
2
=
1
3+2
2
x+
x
1
=3−2
2
+3+2
2
=6
Squaring on 60th sides.
(x+
x
1
)
2
=36
x
2
+
x
2
1
=36−2⇒x
2
+
x
2
1
=34
Squaring on 60th sides.
(x
2
+
x
2
1
)
2
=(34)
2
x
4
+
x
4
1
=1156−2⇒x
4
+
x
4
1
=1154.
solution
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Step-by-step explanation: