用因式分解来解方程(1)9/4(2X+3)²=25/36(12X-18)²(2)(X-根号2)=根号
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用因式分解来解方程
(1)9/4(2X+3)²=25/36(12X-18)²
(2)(X-根号2)=根号5X(2-根号2)
(3)(X-5)(X-3)+X(X+6)=-17
(4)5X²-4X-1/4=X²+31/4
(1)9/4(2X+3)²=25/36(12X-18)²
(2)(X-根号2)=根号5X(2-根号2)
(3)(X-5)(X-3)+X(X+6)=-17
(4)5X²-4X-1/4=X²+31/4
(1)9/4(2X+3)^2=25/36(12X-18)^2
(3/2(2X+3))^2-(5/6(12X-18))^2=0
((3/2(2X+3))-(5/6(12X-18)))*((3/2(2X+3))+(5/6(12X-18)))=0
(3X+9/2-10X+15)*(3X+9/2+10X-15)=0
(39/2-7X)*(13X-21/2)=0
7X=39/2,X=39/14
13X=21/2,X=21/26
(2)(X-根号2)=根号5X(2-根号2)
(X-2^0.5)=(5^0.5)X(2-2^0.5)
(X-2^0.5)-(5^0.5)X(2-2^0.5)=0
X-2^0.5-2*(5^0.5)X-(10^0.5)*X=0
(1-2*(5^0.5)-(10^0.5))*X-2^0.5=0
X=(2^0.5)/(1-2*(5^0.5)-(10^0.5))
(3)(X-5)(X-3)+X(X+6)=-17
(X-5)(X-3)+X(X+6)=-17
X^2-5X-3X+15+X^2+6X+17=0
2X^2-2X+32=0
X^2-X+16=0
X1=1/2+(1/4-32)^0.5=1/2+(1-128)^0.5/2=(1+(-127)^0.5)/2=(1+i*127^0.5)/2
X2=1/2-(1/4-32)^0.5=1/2-(1-128)^0.5/2=(1-(-127)^0.5)/2=(1-i*127^0.5)/2
(4)5X²-4X-1/4=X²+31/4
5X^2-4X-1/4=X^2+31/4
4X^2-4X-1/4-31/4=0
4X^2-4X-8=0
X^2-X-2=0
(X-2)(X+1)=0
X1=2
X2=-1
(3/2(2X+3))^2-(5/6(12X-18))^2=0
((3/2(2X+3))-(5/6(12X-18)))*((3/2(2X+3))+(5/6(12X-18)))=0
(3X+9/2-10X+15)*(3X+9/2+10X-15)=0
(39/2-7X)*(13X-21/2)=0
7X=39/2,X=39/14
13X=21/2,X=21/26
(2)(X-根号2)=根号5X(2-根号2)
(X-2^0.5)=(5^0.5)X(2-2^0.5)
(X-2^0.5)-(5^0.5)X(2-2^0.5)=0
X-2^0.5-2*(5^0.5)X-(10^0.5)*X=0
(1-2*(5^0.5)-(10^0.5))*X-2^0.5=0
X=(2^0.5)/(1-2*(5^0.5)-(10^0.5))
(3)(X-5)(X-3)+X(X+6)=-17
(X-5)(X-3)+X(X+6)=-17
X^2-5X-3X+15+X^2+6X+17=0
2X^2-2X+32=0
X^2-X+16=0
X1=1/2+(1/4-32)^0.5=1/2+(1-128)^0.5/2=(1+(-127)^0.5)/2=(1+i*127^0.5)/2
X2=1/2-(1/4-32)^0.5=1/2-(1-128)^0.5/2=(1-(-127)^0.5)/2=(1-i*127^0.5)/2
(4)5X²-4X-1/4=X²+31/4
5X^2-4X-1/4=X^2+31/4
4X^2-4X-1/4-31/4=0
4X^2-4X-8=0
X^2-X-2=0
(X-2)(X+1)=0
X1=2
X2=-1
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