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1x =a ² +b ² − a ² −b²
a 2 +b ²+ a² −b²
⇒ x−1x+1 = a 2+b 2 + a
2 −b ² − a 2 +b² + a ² −b²a ² +b ² + a ²−b ²+ a ² +b ² − a ² −b²
⇒ x−1x+1 = a ² −b ²a ² +b ²
⇒( x−1x+1 ) 2 = a ² −b ²a ²+b ²
⇒(x+1) 2 (a ² −b ² )=(a ² +b ² )(x−1) ²
⇒(x ² +1+2x)(a 2 −b² )=(x ²+1−2x)+(a 2 +b ²)
⇒x ² a ²−x ²b ² +a ²−b ² +2xa 2−2xb =x ²a²+x² b²+a ² +b²
−2xa 2 −2xb ²
⇒4xa ² =2x ² b ² +2b ²
⇒2xa ² =(x² b²+b2)
⇒b² (x 2 +1)=2xa²
⇒b² = x² +1 / 2xa² .
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