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4. a) (x+1)² + (x+2)² = x² + 2x + 1 + x² + 4x + 4 = 2x² + 6x + 5
b) (x+3)²+(x-2)² = x² + 6x + 9 + x² - 4x - 4 = 2x² + 2x + 5
c) (x-4)² - (x+4)² = x² - 8x + 16 - x² - 8x - 16 = -16x
d) (x-3)³ - (x-1)² = x² - 6x + 9 - x² + 2x - 1 = 8 - 4x
e) (2x-1)²+(2x-3)² = 4x² - 4x + 1 + 4x² - 12x + 3 = 8x² - 16x + 4
f) (2x+1)² - (3x-1)²= 4x² + 4x + 1 - 9x² + 6x - 1 = 10x - 5x²
8. a) (√2+1)²+ (√2-1)² = 2+2√2+1+2-2√2+1 = 6
b) (2+√3)² - (2-√3)² = 4 + 4√3 + 3 - 4 + 4√3 - 3 = 8√3
c) (2√3-1)² - (√3+2)² = 12 - 4√3 + 1 - 3 - 4√3 - 4 = 6 - 8√3
d) (2√3-1)²+(2√3+1)² = 12 - 4√3 + 1 + 12 + 4√3 +1 = 26
9. c)![\frac{2}{2\sqrt{3}-4}*\frac{2\sqrt{3}+4}{2\sqrt{3}+4}=\frac{4\sqrt{3}+8}{12-16}=\frac{4\sqrt{3}+8}{-4}=-\sqrt{3}-8 \frac{2}{2\sqrt{3}-4}*\frac{2\sqrt{3}+4}{2\sqrt{3}+4}=\frac{4\sqrt{3}+8}{12-16}=\frac{4\sqrt{3}+8}{-4}=-\sqrt{3}-8](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B2%5Csqrt%7B3%7D-4%7D%2A%5Cfrac%7B2%5Csqrt%7B3%7D%2B4%7D%7B2%5Csqrt%7B3%7D%2B4%7D%3D%5Cfrac%7B4%5Csqrt%7B3%7D%2B8%7D%7B12-16%7D%3D%5Cfrac%7B4%5Csqrt%7B3%7D%2B8%7D%7B-4%7D%3D-%5Csqrt%7B3%7D-8)
d)![\frac{2\sqrt{3}}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}=\frac{6-2\sqrt{3}}{3-1}=\frac{6-2\sqrt{3}}{2}=3-2\sqrt{3} \frac{2\sqrt{3}}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}=\frac{6-2\sqrt{3}}{3-1}=\frac{6-2\sqrt{3}}{2}=3-2\sqrt{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B3%7D%2B1%7D%2A%5Cfrac%7B%5Csqrt%7B3%7D-1%7D%7B%5Csqrt%7B3%7D-1%7D%3D%5Cfrac%7B6-2%5Csqrt%7B3%7D%7D%7B3-1%7D%3D%5Cfrac%7B6-2%5Csqrt%7B3%7D%7D%7B2%7D%3D3-2%5Csqrt%7B3%7D)