Question

solve it
correctly
no illogical answers​

Answer 1

Answer:

(8). 62 ; (9). 27

Step-by-step explanation:

8). x + $\frac{1}{x}$ = 8 ( x ≠ 0 ) ....... (1)

(1) × x

x² - 8x + 1 = 0

D = (- 8)² - 4(1)(1) = 60 = ( 2√15)²

$x_{1}$ = (8 + 2√15) ÷ 2 = 4 + √15

$x_{2}$ = (8 - 2√15) ÷ 2 = 4 - √15

(4 + √15)² = 16 + 8√15 + 15 = 31 + 8√15

(31 + 8√15) + $\frac{1}{31+8\sqrt{15} }$ = 31 + 8√15 + $\frac{31-8\sqrt{15} }{31^2 - (8\sqrt{15})^2 }$ = 62

9). a² - 5a - 1 = 0

D = 25 + 4 = 29 = (√29)²

$a_{1}$ = (5 + √29) ÷ 2

$a_{2}$ = (5 - √29) ÷ 2

(5 + √29)² = 25 + 10√29 + 29 = 54 + 10√29

$\frac{27+ 5\sqrt{29} }{2}$ + $\frac{2}{27+5\sqrt{29} }$ = $\frac{27+ 5\sqrt{29} }{2}$ + $\frac{2(27-5\sqrt{29}) }{4}$ = 27

Answer 2

Answer:

8)62,9)27

Step-by-step explanation:

8)x+1/x=8

Squaring on both sides

(x+1/x)^2=8^2 [ :(a+b)^2=a^2+b^2+2ab]

x^2+1/x^2+2.x.1/x=64

x^2+1/x^2+2=64

x^2+1/x^2=64-2

x^2+1/x^2=62.

9)a-1/a=5

Squaring on both sides

(a-1/a)^2=5^2 [:(a-b)^2=a^2+b^2-2ab]

a^2+1/a^2-2.a.1/a=25

a^2+1/a^2-2=25

a^2+1/a^2=25+2

a^2+1/a^2=27