Algebra> m=2-(3)^(1/2) Find the value of (m^6+m^5+...

m=2-(3)^(1/2)
Find the value of (m^6+m^5+m^4+1)/m^3

Aditi , 10 Years ago

Grade 12th pass

7 Answers

SHAIK AASIF AHAMED

Last Activity: 10 Years ago

Hello student,
Please find the answer to your question below
as m= $2-\sqrt{3}$
m²=7- $4\sqrt{3}$
m³=26-15 $\sqrt{3}$
1/m³=26+15 $\sqrt{3}$
Given (m⁶+m⁵+m⁴+1)/m³=m+m²⁺m³+1/m^{3
=2-+7-4+26-15+26+15
=61-5}

Aditi

Last Activity: 10 Years ago

Is there any shorter way to solve this?
i got this question in an aptitude test which had 30 questions for 30 minutes.. so i am supposed to solve this in like a minute or so..

Aditi

Last Activity: 10 Years ago

is there any shorter way of solving this?

Aditi

Last Activity: 10 Years ago

is therr any shorter way of answering this?

mycroft holmes

Last Activity: 10 Years ago

Wish I could post the solution, but this site has a primitive editor

mycroft holmes

Last Activity: 10 Years ago

m = 2 – 3^(1/2), and so m + 1/m = 4.

We can also write this last equation as m^2 = 4m-1

Given expression = (m^3+1/m^3) +m^2+m

Now, using the identity: a+b+c = 0 implies a^3+b^3+c^3 = 3abc, we have

m + 1/m – 4 implies m^3 + 1/m^3 – 64 = 3 (m) (1/m) (-4) = -12

so that m^3 + 1/m^3 = 64-12 = 52.

Also m^2+m = (4m-1)+m = 5m-1 = 9 – 5(2^1/2)

Adding up we get the given expressions equals 61 – 5 (2^1/2)

SHAIK AASIF AHAMED

Last Activity: 10 Years ago

Hello student,
This may help you
m = 2 – 3^(1/2), and rationalising this we get m + 1/m = 4. som^2 = 4m-1
Given equation is= (m^3+1/m^3) +m^2+m
From the identity if a+b+c = 0 gives a^3+b^3+c^3 = 3abc,
we havem + 1/m – 4=0 gives m^3 + 1/m^3 – 64 = 3 (m) (1/m) (-4) = -12
so m^3 + 1/m^3 = 64-12 = 52.
Also m^2+m = (4m-1)+m = 5m-1 = 9 – 5(3^1/2)
so m+m²+m³+1/m³=61 – 5 (3^1/2)