If x=1+√2+√3, then x4−4x3−4x2+16x=?
Answer:
8
- Given: x=1+√2+√3
According to the question, we need to find the value of x=1+√2+√3 - x=1+√2+√3⟹x−1=√2+√3
Taking the square on both sides
x2+1−2x=2+3+2×√2×√3 [ Using (a+b)2=a2+b2+2ab]⟹x2−2x−4=2√6 - Again, taking the square on both sides
x4+4x2+16−4x3+16x−8x2=4×6 [∵(a−b−c)2=a2+b2+c2−2ab+2bc−2ca]⟹x4−4x3−4x2+16x+16=24⟹x4−4x3−4x2+16x=8