$\text{Given that,}\\\\x^2 + \dfrac1{x^2} = 38\\\\\\(i)\\\\\left(x-\dfrac 1x \right)^2 = x^2 + \dfrac 1{x^2} - 2 \cdot x \cdot \dfrac 1x\\\\\\\implies \left(x-\dfrac 1x \right)^2 = 38 -2 = 36\\\\\implies x - \dfrac 1x = \pm\sqrt{36} = \pm 6 \\\\\\(ii)\\\\x^2 + \dfrac 1{x^2} = 38\\\\\\\implies \left(x^2 + \dfrac 1{x^2} \right)^2 = 38^2\\\\\\\implies x^4 + \dfrac 1{x^4} + 2\cdot x^2 \cdot \dfrac 1{x^2} = 1444\\\\\\\implies x^4 + \dfrac 1{x^4} + 2 = 1444\\\\\\$

$\implies x^4 +\dfrac 1{x^4} = 1444-2 = 1442$

7 0

2 years ago

6 = 2(y + 2) Solve for y

egoroff_w [7]

Awnser: y=1
Distribute
6=2(y+2)
6=2y+4
subtract 4 from both sides of the equation
6=2y+4
6-4=2y+4-4
simply
2=2y
then divide 2 from both sides
2/2=2y/2
y=1
Hope this helps :)

5 0

3 years ago

Complete the sequence: 1, 1, 2, 3, 5, ____, ____, ____.

Elza [17]

Answer:

8, 13, 21

Step-by-step explanation:

This is a part of the Fibonacci sequence. it is where you add the two previous numbers together to get the third.

Ex.

1+1 = 2

1+2 = 3

7 0

4 years ago