Mister Exam
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How to use it?
- Equation:
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Equation 3x-1=2x
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Equation -x^2+6*x-7=0
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Equation -x^3+4*x^2+4*x-16=0
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Equation x/7=6
- Express {x} in terms of y where:
- -10*x+4*y=16
- -18*x-6*y=10
- -2*x-3*y=10
- 10*x+12*y=-12
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Identical expressions
- (sqrt(five)*b/ two + four (sqrt(three)+ three))^ two =(b+ six *(one +sqrt(three)))^ two +(b/ two + two *(sqrt(three)+ three))^ two
- ( square root of (5) multiply by b divide by 2 plus 4( square root of (3) plus 3)) squared equally (b plus 6 multiply by (1 plus square root of (3))) squared plus (b divide by 2 plus 2 multiply by ( square root of (3) plus 3)) squared
- ( square root of (five) multiply by b divide by two plus four ( square root of (three) plus three)) to the power of two equally (b plus six multiply by (one plus square root of (three))) to the power of two plus (b divide by two plus two multiply by ( square root of (three) plus three)) to the power of two
- (√(5)*b/2+4(√(3)+3))^2=(b+6*(1+√(3)))^2+(b/2+2*(√(3)+3))^2
- (sqrt(5)*b/2+4(sqrt(3)+3))2=(b+6*(1+sqrt(3)))2+(b/2+2*(sqrt(3)+3))2
- sqrt5*b/2+4sqrt3+32=b+6*1+sqrt32+b/2+2*sqrt3+32
- (sqrt(5)*b/2+4(sqrt(3)+3))²=(b+6*(1+sqrt(3)))²+(b/2+2*(sqrt(3)+3))²
- (sqrt(5)*b/2+4(sqrt(3)+3)) to the power of 2=(b+6*(1+sqrt(3))) to the power of 2+(b/2+2*(sqrt(3)+3)) to the power of 2
- (sqrt(5)b/2+4(sqrt(3)+3))^2=(b+6(1+sqrt(3)))^2+(b/2+2(sqrt(3)+3))^2
- (sqrt(5)b/2+4(sqrt(3)+3))2=(b+6(1+sqrt(3)))2+(b/2+2(sqrt(3)+3))2
- sqrt5b/2+4sqrt3+32=b+61+sqrt32+b/2+2sqrt3+32
- sqrt5b/2+4sqrt3+3^2=b+61+sqrt3^2+b/2+2sqrt3+3^2
- (sqrt(5)*b divide by 2+4(sqrt(3)+3))^2=(b+6*(1+sqrt(3)))^2+(b divide by 2+2*(sqrt(3)+3))^2
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Similar expressions
- (sqrt(5)*b/2+4(sqrt(3)+3))^2=(b+6*(1+sqrt(3)))^2+(b/2-2*(sqrt(3)+3))^2
- (sqrt(5)*b/2+4(sqrt(3)+3))^2=(b+6*(1+sqrt(3)))^2+(b/2+2*(sqrt(3)-3))^2
- (sqrt(5)*b/2+4(sqrt(3)+3))^2=(b+6*(1+sqrt(3)))^2-(b/2+2*(sqrt(3)+3))^2
- (sqrt(5)*b/2+4(sqrt(3)+3))^2=(b+6*(1-sqrt(3)))^2+(b/2+2*(sqrt(3)+3))^2
- (sqrt(5)*b/2-4(sqrt(3)+3))^2=(b+6*(1+sqrt(3)))^2+(b/2+2*(sqrt(3)+3))^2
- (sqrt(5)*b/2+4(sqrt(3)-3))^2=(b+6*(1+sqrt(3)))^2+(b/2+2*(sqrt(3)+3))^2
- (sqrt(5)*b/2+4(sqrt(3)+3))^2=(b-6*(1+sqrt(3)))^2+(b/2+2*(sqrt(3)+3))^2
(sqrt(5)*b/2+4(sqrt(3)+3))^2=(b+6*(1+sqrt(3)))^2+(b/2+2*(sqrt(3)+3))^2 equation
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The solution
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2 / ___ \ 2 2 |\/ 5 *b / ___ \| / / ___\\ /b / ___ \\ |------- + 4*\\/ 3 + 3/| = \b + 6*\1 + \/ 3 // + |- + 2*\\/ 3 + 3/| \ 2 / \2 /
$$\left(\frac{\sqrt{5} b}{2} + 4 \left(\sqrt{3} + 3\right)\right)^{2} = \left(b + 6 \left(1 + \sqrt{3}\right)\right)^{2} + \left(\frac{b}{2} + 2 \left(\sqrt{3} + 3\right)\right)^{2}$$
Detail solution
Given the equation:
Expand expressions:
Reducing, you get:
Expand brackets in the left part
Divide both parts of the equation by (-18*b - 14*b*sqrt(3) + 4*b*sqrt(15) + 12*b*sqrt(5))/b
We get the answer: b = 0
(sqrt(5)*b/2+4*(sqrt(3)+3))^2 = (b+6*(1+sqrt(3)))^2+(b/2+2*(sqrt(3)+3))^2
Expand expressions:
192 + 96*sqrt(3) + 5*b^2/4 + 4*b*sqrt(15) + 12*b*sqrt(5) = (b+6*(1+sqrt(3)))^2+(b/2+2*(sqrt(3)+3))^2
(sqrt(5)*b/2+4*(sqrt(3)+3))^2 = 144 + b^2 + 12*b + 72*sqrt(3) + 12*b*sqrt(3) + (b/2 + 2*(sqrt(3) + 3))^2
(sqrt(5)*b/2+4*(sqrt(3)+3))^2 = 144 + b^2 + 12*b + 72*sqrt(3) + 12*b*sqrt(3) + 48 + 6*b + 24*sqrt(3) + b^2/4 + 2*b*sqrt(3)
Reducing, you get:
-18*b - 14*b*sqrt(3) + 4*b*sqrt(15) + 12*b*sqrt(5) = 0
Expand brackets in the left part
-18*b - 14*b*sqrt3 + 4*b*sqrt15 + 12*b*sqrt5 = 0
Divide both parts of the equation by (-18*b - 14*b*sqrt(3) + 4*b*sqrt(15) + 12*b*sqrt(5))/b
b = 0 / ((-18*b - 14*b*sqrt(3) + 4*b*sqrt(15) + 12*b*sqrt(5))/b)
We get the answer: b = 0