Question

(2x+1/x+1)⁴-6(2x+1/x+1)²+8=0​

Answer 1

Step-by-step explanation:

let,

2x+1/x+1 = m

${m}^{4} - 6 {m}^{2} + 8 = 0 \\ {m}^{4} - 4 {m}^{2} - 2 {m}^{2} + 8 \\ {m}^{2} ( {m}^{2} - 4) - 2( {m}^{2} - 4) \\ ( {m}^{2} - 4)( {m}^{2} - 2)$

therefore ,

m²=4 m²= 2

m = +- 2 m²= +-√2

Answer 2

Answer:

2x+1/x+1 = m

\begin{lgathered}{m}^{4} - 6 {m}^{2} + 8 = 0 \\ {m}^{4} - 4 {m}^{2} - 2 {m}^{2} + 8 \\ {m}^{2} ( {m}^{2} - 4) - 2( {m}^{2} - 4) \\ ( {m}^{2} - 4)( {m}^{2} - 2)\end{lgathered}m4−6m2+8=0m4−4m2−2m2+8m2(m2−4)−2(m2−4)(m2−4)(m2−2)

therefore ,

m²=4 m²= 2

m = +- 2 m²= +-√2