If x = 1 + √2 + √3 , then the value of (2x⁴ −

Solution

X = 1+ √2+√3  X -1 = √2+√3            both side squaring….  (x-1) ² = (√2+ √3) ² x²+ 1 - 2x = 5 + 2 √6 x² -2x = 4+2√6…… (1) both sides squaring…. (x² -2x-4) ² = (2√6) ² x⁴+ 4x² -4x³+16+16x-8x² = 24 …. (2) x⁴-4x³-4x²+16x-8=0 multiply by 2. 2x⁴-8x³-8x²+32x-16=0 2x⁴-8x³-5x²+26x-28=3x²-6x-12 now – putting the value of equal. (1) and equal (2) =3(x-2x)-12 =3(4+2√6)-12 =12+6√6-12=6√6   After solving we will get it reduced to 6√6