Question

(2-√5/2+√5)^2 - (2+√5/2-√5)^2

Answer 1

[(2- √5)/(2+√5)]² - [(2+√5)/(2- √5)]²

=(2- √5)²/(2+√5)² - (2+√5)²/(2- √5)²

=[(2- √5)²(2 - √5)² - (2+√5)²(2+√5)²]/(2+√5)²(2-√5)²

=[(2 - √5)⁴ - (2+√5)⁴]/[(2+√5)(2- √5)]²

=[(2- √5)⁴ - (2+√5)⁴]/ (2² - √5²)

=[(2-√5)⁴ - (2+√5)⁴] / (4 - 5)

=[(2-√5)⁴ - (2+√5)⁴]/(-1)

=(2+√5)⁴ - (2-√5)⁴

=2⁴+(√5)⁴ + 4(2)³(√5) + 4(2)(√5)³ + 6(2)²(√5)² - [2⁴ + (√5)⁴ + 6(2)²(√5)² - 4(2)³(√5) - 4(2)(√5)³]

=8(2)³(√5) + 8(2)(√5)³

=8×8×√5 + 8×2×5

=64√5 + 80

Answer 2

Answer:

=2√5

Step-by-step explanation:

(2-√5/2+√5)^2 - (2+√5/2-√5)^2

=(2+√5-√5/2)^2 - (2+√5/2-√5)^2

=(2+√5/2)^2 - (2-√5/2)^2 (its in the for a^2 - b^2)

=((2+√5/2)+(2-√5/2)) x ((2+√5/2)-(2-√5/2))

=(2) x (√5)

=2√5