Question

if x-1/2x=3,find the value of x^2+1/4x^2​

Answer 1

Step-by-step explanation:

$\huge\bold{\underline{\underline{\blue{ANSWER}}}}$

x + 1/2x = 2, or

2x^2+1=4x, or

2x^2–4x+1=0

x1 = [4+{16–8)^0.5]/4

= [4+8^0.5]/4

= 1.707106781

x2 = [4-{16–8)^0.5]/4

= [4-8^0.5]/4

= 0.292893216

Therefore (8x^3)+(1/x^3)

= (8*1.707106781^3)+(1/1.707106781^3)

= 39.79898986 + 0.201010126

= 40.

OR

(8x^3)+(1/x^3)

= (8*0.292893216^3)+(1/0.292893216^3)

= 0.201010126 + 39.79899102

= 40.

Answer is 40.

Answer 2

Answer:

Step-by-step explanation:

Given that, x-1/2x =3, then x^2 +1/4x^2 =?

(x-1/2x)^2 =3^2 Squaring both side and expanding by the rule

(a-b)^2  = a^2 +b^2 -2ab

Therefore,

x^2 + (1/2x)^2 - 2*x *(1/2x) =9

x^2 + 1/4x^2 -2 *(1/2) = 9  as x cancel out

x^2 +1/4x^2 -1 = 9

x^2 +1/4x^2 9+1 =10