If x3 +1/x3 =2 find (x+ 1/x) 2 Factorize : (i) x4 + x2 +1 (ii) X4 +4 - Maths - Polynomials

Question

If x3 +1/x3 =2 find (x+ 1/x) 2 Factorize : (i) x4 +
x2 +1 (ii) X4 +4

Manbar Singh · Accepted Answer

i We have, x3 + 1x3 = 2 1We know that, x3 - 1x32 = x3 + 1x32 - 4 x3
× 1x3⇒ x3 - 1x32 = 22 - 4⇒ x3 - 1x32 = 4 -
4⇒ x3 - 1x32 = 0⇒ x3 - 1x3 = 0 2Adding 1 & 2, we
get, 2x3 = 2⇒ x3 = 1⇒ x = 1⇒ 1x = 1Therefore, x +
1x = 1 + 1 = 2Hence, x + 1x = 2

ii x4 + x2 + 1= x4 + x2 + x2 + 1 - x2= x4 + 2x2 + 1 - x2= x4 + 2x2
+ 1 -x2= x2 + 12 - x2= x2 + 1 + x x2 + 1 - x using a2 - b2 = a + b
a - b= x2 + x + 1 x2 - x + 1iii x4 + 4=x4 + 4x2 + 4 - 4x2=x4 + 4x2
+ 4 - 4x2=x22 + 2x22 + 22 - 2x2=x2 + 22 - 2x2=x2 + 2 + 2xx2 + 2 -
2x

If x3 +1/x3 =2 find (x+ 1/x) 2. Factorize : (i) x4 + x2 +1 (ii) X4 +4

If x3 +1/x3 =2 find (x+ 1/x) 2. Factorize : (i) x⁴ + x² +1 (ii) X⁴ +4