If \(x = 3 - \sqrt{3}\), find \(x^2 + \frac{36}{x^2}\)

Assessment: JAMB UTME - Mathematics - 1992 Subject: General Mathematics

Question 1 Report

If \(x = 3 - \sqrt{3}\), find \(x^2 + \frac{36}{x^2}\)

Answer Details
x = 3 -  3
x2 = (3 -  3 )2
= 9 + 3 - 6 34
= 12 - 6 3
= 6(2 -  3 )
∴ x2 +  36 x 2  = 6(2 -  3 ) +  36 6 ( 2 − 3 )
6(2 -  3 ) +  6 2 − 3  = 6(-  3 ) +  6 ( 2 + 3 ) ( 2 − 3 ) ( 2 + 3 )
= 6(2 -  3 ) +  6 ( 2 + 3 ) 4 − 3
6(2 -  3 ) + 6(2 +  3 ) = 12 + 12
= 24

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