Solucionario De Matematica 1 Edwin Galindo
Solve the following equation:
x²-27 = 12
The solution is -2 or 17. There are two solutions to this equation because 27 can be factorized in many ways: 5×3, 3×5, and 3×3. As a result, we have two sets of solutions: x= -2 and x=17. The only difference between the solutions is that one has plus sign and one has a minus sign. They both take you to the same answer though because plus or minus 2 from any other number always give you the same answer (12). So it doesn’t really matter which solution you choose as long as you get to 12. Let us use formulas to solve this equation.
So, we can use the quadratic formula to solve this equation:
x = -b ± b·√(4ac)/2a or x = a·√(4c-4b²) / 2a.
Since a=27 and c=12, we can use the second formula:
x = 27·√(4×12-4×(-2))/2 or x = 27·7 ≈ 17. So our solutions are the same as before.
Solve the following equation: 2x+8=36.
We have three different possible solutions: x= –8, –5 and –3. This is because we can factorize 2×2 into 24x+8, 8x+4 and 4x+2. We have three sets of solutions:
x = –8, –5 and –3 because 2(–8) + 8 = 36, 2(–5) + 8 = 36 and 2(–3) + 8 = 36. So we know that the only difference between the solutions is whether they have a plus or a minus sign. We also know that whatever the sign is, it has no effect on the answer which is always going to be 36. For example x= –3+8=-1 ≈ -1 and x=-3-8=-11 ≈ -11. They give us different answers but they both take us to 36.
So we can use the quadratic formula to solve this equation: x = a ± b ± c.
We have a=36 and b=8 and c=5. So we can use the first formula: x = 36 ± 5 ± 8.
x= -3+5=-1 ≈ -1, x= -3-5=-4 ≈ -4, x=-3+8=-9 ≈ 9. So our solutions are the same as before.
Solve the given equation: a²-b²+c² = 25-2ab+2ac.
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