Question

X= 3+√5 then find the value of x^4- 12x^3 + 44x^2 - 48x +17

Answer 1

Answer:

X=3+√5

to find x^4 - 12 x^3+44x^2-48x+17

we put the value of X

=(3+√5)^4-12(3+√5)^3+44(3+√5)^2-48(3+√5)+17

=81+25-12(27+5√5)+44(9+5)-144+48√5+17

=81+25-324-60√5+396+220-192√5+17

=81+25-324+396+220+17-60√5-192√5

=415-252√5

=163√5

Answer 2

Answer:

Step-by-step explanation:

x= 3 + √5

x-3 = √5

Taking square on both side

(x-3)²= (√5)²

x²-6x+9 = 5

Therefore, x²-6x-4=0 (1)

Now

Divide

x⁴-12x³+44x²-48x+17 by x²-6x-4

So finally

x²(x²-6x+4)-6x(x²-6x+4)+4(x²-6x+4)+1

=1. ___(from 1)

Most proper way for JEE