Respuesta :
Answer:
Step-by-step explanation:
(2x-1)²=x²+4²
4x²-4x+1=x²+16
3x²-4x-15=0
a=3 b=-4 c= -15
D=b²-4ac
=16-4*3*(-15)=196
x1=-b+√D/2a=4+14/6=3
x2=-b-√D/2a=4-14/6=-10/6=-5/3
Answer:
x = 3
Step-by-step explanation:
Using Pythagoras' theorem on the right triangle, then
(2x - 1)² = 4² + x² ← expand parenthesis on the left side and simplify
4x² - 4x + 1 = 16 + x² ( subtract 16 + x² from both sides )
3x² - 4x - 15 = 0 ← in standard form
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 15 = - 45 and sum = - 4
The factors are - 9 and + 5
Use these factors to split the x- term
3x² - 9x + 5x - 15 = 0 ( factor the first/second and third/fourth terms )
3x(x - 3) + 5(x - 3) ← factor out (x - 3)
(x - 3)(3x + 5) = 0
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - [tex]\frac{5}{3}[/tex]
However, x must be greater than zero
Hence x = 3 cm
