Show that y^2-4y-2=0
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To show that y^2 - 4y - 2 = 0, we will use the quadratic formula.
The quadratic formula is given as:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, the coefficients are as follows:
a = 1 (coefficient of y^2)
b = -4 (coefficient of y)
c = -2 (constant term)
We will substitute these values into the quadratic formula and solve for y.
y = (4 ± √((-4)^2 - 4(1)(-2))) / (2(1))
Now, let's simplify the equation further:
y = (4 ± √(16 + 8)) / 2
y = (4 ± √24) / 2
y = (4 ± √(4 × 6)) / 2
y = (4 ± 2√6) / 2
Now, we can simplify the expression:
y = 2 ± √6
So the solutions for y are:
y = 2 + √6
y = 2 - √6
Thus, we have shown that y^2 - 4y - 2 = 0 has two solutions: y = 2 + √6 and y = 2 - √6.