Question

Help pls am confused ​

Answer 1

Given, x−x1=5

Squaring both the sides,

⇒(x−x1)2=52

⇒x2+x21−2(x)(x1)=25

⇒x2+x21=25+2

⇒x2+x21=27

Now,

x3−x31

=(x−x1)[(x)2+(x1)2+(x)(x1)]

=5(27+1)

=140

Answer 2

9514 1404 393

Answer:

322

Explanation:

Consider the cube ...

(a +b)³ = a³ +3a²b +3ab² +b³

= a³ +b³ +3ab(a+b)

Now, for a=x and b=1/x, we have ...

(x +1/x)³ = x³ +1/x³ +3(x)(1/x)(x +1/x)

Using the known value for x+1/x, this is ...

7³ = x³ +1/x³ +3(7)

x³ +1/x³ = 7³ -3·7 = 343 -21

x³ +1/x³ = 322

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If you want to try this with numbers, the solutions to the original equation are ...

x ≈ 6.85410196625 and its reciprocal.