Question

X+1/4x = 1/2
X^6 + 1/64x^4 =?
​

Answer 1

Answer:

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Step-by-step explanation:

We have,

f(x)=64x

3

+

x

3

1

α and β be the roots

4x+

x

1

=2 ………(1)

On cube both side and we get,

(4x+

x

1

)

3

=2

3

(4x)

3

+(

x

1

)

3

+3×4x×

x

1

(4x+

x

1

)=8

64x

3

+

x

3

1

+12(4x+

x

1

)=8

f(x)+12×2=8

f(x)+24=8

f(x)=8−24

f(x)=−16

Now,

α and β are the roots

f(α)=f(β)=−16

Hence, this is the answer.

Answer 2

Step-by-step explanation:

x+1/4x = 1/2

5/4x = 1/2

10x = 4

x = 4/10

x = 2/5

now x^6 + 1/64x^4

putting x = 2/5 in equation

(2/5)^6 + 1/64*(2/5)^4

(2/5)^6 + (1/64)*(16/625)

(2/5)^6 + (1/4)*(1/625)

(2/5)^6 + (1/2500)

(2/5)^6 + (1/5^4*2^2)

133/13040

iam not sure about it, if wrong please correct me.