Pythagoras Theorem and Quadratic Equations

Solve for x:

a = (x-2)

b = 9

c = (x+1)

Step-by-step explanation:

Pythagoras theorem

a^2=b^2+c^2

(x-2) ^2=9^2 + (x+1) ^2

x^2-4x+4=81+x^2+2x+1

Collect like terms

-4x-2x=82-4

-6x=78

x=-13

x = - 13

Step-by-step explanation:

using Pythagoras theorem which says that the square of the hyponeneus side of a right angled triangle is equal to the sum of square of the two opposite sides.

mathematically,

|H|² = |OPP|² + |ADJ|²

H = (x-2), opp = 9 adj = (x+1)

(x-2) ² = (9) ² + (x+1) ²

x² - 4x + 4 = 81 + x²+2x+1

collecting the like terms

x² - x² - 4x-2x = 81 + 1 - 4

- 6x = 89 - 4

-6x = 78

divide both sides by the coefficient of x which is - 6

-6x/-6 = 78/-6

x = - 13