Question

If x = 1 + √2 + √3; then find 2x⁴ - 8x³ - 5x² + 26x - 28
A) 6 √6
B) 3 √6
C) 2 √6
D) 0​

Answer 1

Answer:

a) 6 root 6

Step-by-step explanation:

see the pictures

Answer 2

Step-by-step explanation:

LET

a=√2→a²=2→a³=2√2→a^4=4

b=√3→b²=3→b³=3√3→b^4=9

ab=√6

a²b+b²a≈2√3+3√2

(x-1)=√2+√3=a+b

(x-1)²=(a+b)²=a²+b²+2ab=5+2√6

(x-1)³=(a+b)³=a³+b³+3(a²b+b²a)=2√2+3√3+6√3+9√2=11√2+9√3

(x-1)^4≈(5+2√6)²=49+20√6

1) x=1+(x-1)=1+√2+√3

② x²=[1+(x-1)]²={1+2(x-1)+(x-1)²}={1+2√2+2√3+5+2√6}=6+2√2+2√3+2√6

③ x³=[1+(x-1)]³

=1+3(x-1)+3(x-1)²+(x-1)³

=1+3√2+3√3+15+6√6+11√2+9√3

=16+14√2+12√3+6√6

④ x^4=[1+(x-1)]^4

=1+4(x-1)+6(x-1)²+4(x-1)³+(x-1)^4

=1+(4√2+4√3)+(30+12√6)

n+(44√2+36√3)+(49+20√6)

=80+48√2+40√3+32√6

∴2x^4–8x³-5x²+26x–28

=160+96√2+80√3+64√6

-128–112√2–96√3–48√6

-30–10√2-10√3–10√6

26+26√2+26√3

-28

Adding...........................

6√6

option a is right answer