Question

(2+√3)⁴-8(2+√3)³+18(2+√3)²-8(2+√3)+2​

Answer 1

Step-by-step explanation:

Answer · 1. i) (3)⁻² = 1/(3)² = 1/9 iv) (6)² = 36 · 2. i) (-4)⁵ / (-4)⁸ = (-4)⁵⁻⁸= (-4)⁻³ = 1/(-4)³ = 1/(-64).

Answer 2

$1$

Step-by-step explanation:

$Given \: ,(2+√3)⁴-8(2+√3)³+18(2+√3)²-8(2+√3)+2 \\ = (2 + \sqrt{3} ) \{ (2+√3)³-8(2+√3)²+18(2+√3)-8\} + 2 \\ = (2 + \sqrt{3} ) \{ {2}^{3} + ( \sqrt{3} )^{3} + 3 \times 2 \times \sqrt{3} (2 + \sqrt{3} ) - 8( {2}^{2} + ( \sqrt{3} )^{2} + 2 \times 2 \times \sqrt{3} ) + 36 + 18 \sqrt{3} - 8\} + 2 \\ = (2 + \sqrt{3} ) \{ 8 + 3 \sqrt{3} + 12 \sqrt{3} + 18 - 8(4 + 3 + 4 \sqrt{3} ) + 36 + 18 \sqrt{3} - 8\} + 2 \\ = (2 + \sqrt{3} ) \{ 54 + 33 \sqrt{3} - 32 - 24 - 32 \sqrt{3} \} + 2 \\ = (2 + \sqrt{3} ) ( \sqrt{3} - 2)+ 2 \\ = ( \sqrt{3} + 2)( \sqrt{3} - 2) + 2 \\ = ( \sqrt{3} )^{2} - {2}^{2} + 2 \\ = 3 - 4 + 2 \\ = 1$