Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation a^2*x^2-21*a^2+a*x+1=0
-
Equation 5-x=4(x-3)
-
Equation exp(x)=0
-
Equation 3^x=8
- Express {x} in terms of y where:
- 9*x-19*y=-20
- 15*x+17*y=-10
- -11*x-18*y=6
- -7*x-5*y=-17
-
Identical expressions
- x- two ^x+ five
- x minus 2 to the power of x plus 5
- x minus two to the power of x plus five
- x-2x+5
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Similar expressions
- x-2^x-5
- x+2^x+5
x-2^x+5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Sum and product of roots
[src]
sum
/-log(2) \
W|--------|
\ 32 /
3 + -5 - -----------
log(2)
$$\left(-5 - \frac{W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}\right) + 3$$
=
/-log(2) \
W|--------|
\ 32 /
-2 - -----------
log(2)
$$-2 - \frac{W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}$$
product
/ /-log(2) \\ | W|--------|| | \ 32 /| 3*|-5 - -----------| \ log(2) /
$$3 \left(-5 - \frac{W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}\right)$$
=
/-log(2) \
3*W|--------|
\ 32 /
-15 - -------------
log(2)
$$-15 - \frac{3 W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}$$
-15 - 3*LambertW(-log(2)/32)/log(2)
Rapid solution
[src]
x1 = 3
$$x_{1} = 3$$
/-log(2) \
W|--------|
\ 32 /
x2 = -5 - -----------
log(2)
$$x_{2} = -5 - \frac{W\left(- \frac{\log{\left(2 \right)}}{32}\right)}{\log{\left(2 \right)}}$$
x2 = -5 - LambertW(-log(2)/32)/log(2)