Question
If x = 1 + √2 + √3 , then the value of (2x⁴ −
8x³ − 5x² + 26x − 28) is ?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
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