- #1
eskil
- 4
- 0
just looking for a quick solution for my equation, seems like my head is just working the wrong way coz I know it's not a hard one:
a2 + a2 = (a + 1)2
a = ?
a2 + a2 = (a + 1)2
a = ?
rock.freak667 said:a2+a2=2a2
expand the right side and then simplify.
eskil said:solved it now
a2 + a2 = a2 + 2a + 1
simplified it to a quadraticequation
0 = -a2 + 2a + 1
a1 = 1 + sq.root of 2
a2 = 1 - sq.root of 2
a2 is negative therefore a1 is the right answer
which gives a = 2,41
The formula for finding a in this equation is a = (a + 1) / 2.
To solve for a, you can use the formula a = (a + 1) / 2. First, simplify the equation by combining like terms on the left side, which gives you 2a2 = (a + 1)2. Then, expand the right side to get 2a2 = a2 + 2a + 1. Finally, subtract a2 and 2a from both sides, which leads to the formula a = (a + 1) / 2.
The logic behind finding a in this equation is based on the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The equation a2 + a2 = (a + 1)2 is essentially a simplified version of the Pythagorean theorem, where a is one of the sides and (a + 1) is the hypotenuse. By solving for a, we are essentially finding the missing side of the right triangle.
Yes, there is one restriction on the value of a in this equation. Since we are dealing with a right triangle, a must be a positive number, as negative lengths do not exist in geometry.
Yes, this formula can be applied to other equations with similar patterns. As long as the equation follows the pattern of a2 + a2 = (a + 1)2, the formula a = (a + 1) / 2 can be used to solve for a. However, if the equation deviates from this pattern, a different formula may be needed to solve for a.