Question

if X=(2+root5)^1/2 +(2-root5)^1/2 and y=(2+root5)^1)2-(2-root5)^1)2then evaluate x^2 + y^2 solving on a paper must be easier​

Answer 1

Your question ,

if X=(2+root5)^1/2 +(2-root5)^1/2 and y=(2+root5)^1)2-(2-root5)^1)2then evaluate x^2 + y^2 solving on a paper must be easier

Your answer ,

82.4721359550302329904704

Explanation ,

Given ,

• X = ( 2 + √5 ) ^ ½ + ( 2 - √5 ) ^ ½

• Y = ( 2 + √5 ) ¹ x 2 - ( 2 - √5 ) ¹ x 2

• X² + Y² = ...?

Finding the value of 'X' ,

• X = ( 2 + √5 ) ^ ½ + ( 2 - √5 ) ^ ½

• X = ( 2 + 2.2360679775 ) ^½ + ( 2 - 2.2360679775 ) ^½

• X = 4.2360679775^ ½ + ( - 0.2360679775) ^ ½

• X = 2.05817102727 - 0.48586827175

• X = 1.57230275552

Finding the value of 'Y'

• Y = ( 2 + √5 ) ¹ x 2 - ( 2 - √5 ) ¹ x 2

• Y = ( 2 + 2.2360679775 ) x 2 - ( 2 - 2.2360679775 ) x 2

• Y = ( 4.2360679775 x 2 ) - ( - 0.2360679775 x 2 )

• Y = 8.472135955 - ( -0.472135955 )

• Y = 8.472135955 + 0.472135955

• Y = 8.94427191

Evaluating X² + Y² ,

• X² + Y² = ( 1.57230275552 )² + ( 8.94427191 )²

• = 2.4721359550157848904704 + 80.0000000000150481

• = 82.4721359550302329904704