Question

Please help me with this maths beast. Will mark the best answer as brainliest.

Answer 1

hope it helps you with the answer

Answer 2

Note: 

(a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2

(a + b)^2 = a^2 + b^2 + 2ab


$Given : x = 1 + \sqrt{2}$

Now,

$x^4 - x^3 - 2x^2 - 3x + 1$

$(1 + \sqrt{2} )^4 - (1 + \sqrt{2} )^3 - 2(1 + \sqrt{2} )^2 - 3(1 + \sqrt{2} ) + 1$

$12 \sqrt{2} + 17 - (5 \sqrt{2} + 7) - 2(2 \sqrt{2} + 3) - 3(1 + \sqrt{2} ) + 1$

$12 \sqrt{2} + 17 - 5 \sqrt{2} - 7 - 2(2 \sqrt{2} + 3) - 3(1 + \sqrt{2} ) + 1$

$12 \sqrt{2} + 17 - 5 \sqrt{2} - 7 - 4 \sqrt{2} -6 - 3(1 + \sqrt{2} ) + 1$

$12 \sqrt{2} + 17 - 5 \sqrt{2} - 7 - 4 \sqrt{2} - 6 - 3 - 3 \sqrt{2} + 1$

$1 - 3 - 3 \sqrt{2} - 4 \sqrt{2} - 5 \sqrt{2} - 6 - 7 + 12 \sqrt{2} + 17$

1 - 3 - 6 - 7 + 17

2.


Hope this helps!