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(2x+3)²=4(2x+3)

12(2x+3)=4(2x+3)²+9, 解:4(2x+3)²-12(2x+3)+9=0, (4x+6)²-2×3×(4x+6)+3²=0, (4x+6-3)²=0, 4x+3=0, x=-3/4

用直接开平方法解方程 (x-1)²=(2x+3)² (x-1)²=(2x+3)² x-1=2x+3 x=-4 或x-1=-(2x+3) x=-2/3

∫x³/(x²+2x-3)dx=∫(x³+2x-3x-2x+3)/(x²+2x-3)dx =∫x+3/(x²+2x-3)dx =∫xdx+3∫1/(x²+2x-3)dx =x²/2+3∫1/[(x-1)(x+1)]dx =x²/2+3/4∫1/(x-1)-1/(x+3)]dx = x²/2+3/4ln|x-1|-3/4ln|x+3|+C

2x²+3=7x, 2x²-7x+3=0, 2[x²-2×(7/4)×x+(7/4)²]=2×(7/4)²-3, 2(x-7/4)²=25/8, (x-7/4)²=25/16, x-7/4=5/4,或x-7/4=-5/4, x=3,或x=1/2

x终边过点(-3,4) cosx=-3/√[(-3)²+4²]=-3/5 sinx=4/√[(-3)²+4²]=4/5 sin2x+cos2x =2sinxcosx+2cos²x-1 =2·(4/5)·(-3/5)+2(-3/5)²-1 =-31/25

解 (x-2)²=(2x+3)² x²-4x+4=4x²+12x+9 即 3x²+16x+5=0 (3x+1)(x+5)=0 ∴x=-5 或x=-1/3

5x²-2x-1/4=x²-2x+3/4 5x²-x²-2x+2x-1/4-3/4=0 4x²-1=0 (2x-1)(2x+1)=0 x=1/2或x=-1/2

x²-2x-3=2x+5 x²-4x-8=0 x²-4x+4=8+4 (x-2)²=12 x-2=±√12 x=±2√3+2

2x^5+7x⁴+12x³+14x²+10x+3 =2x^5+2x⁴+5x^4+5x³+7x³+7x²+7x²+7x+3x+3 =2x⁴(x+1)+5x³(x+1)+7x²(x+1)+7x(x+1)+3(x+1) =(x+1)(2x⁴+5x³+7x²+7x+3) =(x+1)(2x⁴+2x&#...

(2x+3)²-5=0 4x²+12x+9-5=0 4x²+12x+4=0 x²+3x+1=0 x=(-3±√5)/2

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