ADVT: SMARTWATCHES IN AMAZON
Consider this quadratic equation
X^2+X = 12
we can solve this equation using pictures
The area of the green square is x*x = x^2. The area of the red rectangle is x*1 =x. The total area, according to the equation is x^2+x =12.
X^2+X = 12
we can solve this equation using pictures
The area of the green square is x*x = x^2. The area of the red rectangle is x*1 =x. The total area, according to the equation is x^2+x =12.
Split the red rectangle into two equal halves. The width of each is 0.5. The total area remains the same.
Move one halved rectangle to the bottom of the square as shown in the figure.
Fill up the extra corner square. Its area is 0.5 *0.5 = 0.25. Now the total area becomes 12.25. The above figure is the perfect square. Hence length *length also gives the area. Therefore, we can write.
(x+0.5) * (x+0.5) = 12.25
or (x+0.5)^2 = 12.25 or
x+0.5 = square root of 12.25.
x+0.5 =3.5=3+0.5
so, x = 3
we got the answer
Other quadratic equations may be solved in this way. Even quadratic formula for x can be derived using pictures -try yourself.
x^2 can be visualized as a square.
x^3 as cube
y=x^2 as a parabola
y=sin x as a wave
Any equation can be modeled as a figure.
y=x^2 as a parabola
y=sin x as a wave
Any equation can be modeled as a figure.
We have learned yet another way to solve the quadratic equation.
solve, 4x^2 +6x-54 = 0
Hint: side of green square must be = 2x, x, and 6 are the sides of the red rectangle.