Pythagorean Quadratic Speech or Presentation Example | Topics and Well Written Essays - 250 words

Pythagorean Quadratic - Speech or Presentation Example Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is ‘x’? Since the Pythagorean Theorem is given by c2 = a2 + b2 then, each of the expressions ‘x’, ‘2x + 4’, and ‘2x + 6’ representing the sides of the right triangle which encloses the route to the buried treasure may be plugged into the Pythagorean equation such that (2x + 6)2 = x2 + (2x + 4)2 where ‘2x + 6’ paces refers to the measure of the longest side. Then expanding the binomials (2x + 6)2 and (2x + 4)2 yields 4x2 + 24x + 36 and 4x2 + 16x + 16, respectively. Upon combining like terms in the compound equation formed, the resulting equation turns out quadratic with x2 - 8x - 20 = 0. By factoring the trinomial, x2 - 8x - 20 becomes the product (x - 10) * (x + 2). Through zero-factor property, each factor may be equated to zero to have x - 10 = 0 and x + 2 = 0, correspondingly. Solving completely, ‘x’ can be isolated on one side of each equation, becoming x = 10 and x = -2. It is logical to use positive values, so in this case, take x = 10. This means from Castle Rock to the place where the treasure is buried, Ahmed can walk 2*(10) + 6 or 26 paces to access the treasure or Vanessa can walk 10 paces heading north first then 2*(10) + 4 or 24 paces going east to be brought to the treasure spot. Apparently, ‘Pythagorean Theorem’ proves useful in solving the specified problem which may be put into an illustration of a closed three-sided figure. Since there are distances covered northward and eastward, a