if a= 4√3+4√2 find 1/a and (a+1/a)2
Answers
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 both sides,
(x+
x
1
)
2
=36
x
2
+
x
2
1
=36−2
⇒x
2
+
x
2
1
=34
Squaring on both sides,
(x
2
+
x
2
1
)
2
=(34)
2
x
4
+
x
4
1
=1156−2
⇒x
4
+
x
4
1
=1154.
ANSWER :–
a⁴ - 1/a⁴ = - 816√2
EXPLANATION :–
GIVEN :–
• a = 3-2√2
TO FIND :–
Value of a⁴ - 1/a⁴.
SOLUTION :–
• According to the question –
⇨ a = 3-2√2
➨ Now let's find 1/a –
⇨ 1/a = [1/(3 - 2√2)][(3 + 2√2)(3 + 2√2)]
⇨ 1/a = (3 + 2√2)/(9 - 8)
⇨ 1/a = 3 + 2√2
➨ Now let's find (a² + 1/a²) –
⇨ (a + 1/a)² = a² + (1/a²) + 2(a)(1/a)
⇨ (6)² = a² + (1/a²) + 2
⇨ 36 = a² + (1/a²) + 2
⇨ a² + 1/a² = 34 —–———eq.(1)
➨ Now let's find (a² - 1/a²) –
⇨ (a² - 1/a²) = (a - 1/a)(a + 1/a)
⇨ a² - 1/a² = (-4√2)(6)
⇨ a² - 1/a² = -24√2 ——–—–eq.(2)
• Now multiply both equations —
➨ (a² + 1/a²)(a² - 1/a² ) = a⁴ - 1/a⁴
➨ a⁴ - 1/a⁴ = (34)(-24√2)
➨ a⁴ - 1/a⁴ = - 816√2
Hey buddy hope it helped you