We have
(a + b)² = a² + 2ab + b²
so that with a = x² and b = 5, we have
x⁴ + 10x² + 25 = (x² + 5)²
Next, we have
a² - b² = (a - b) (a + b)
so that with a = x and b = √5 i,
x² + 5 = x² - (-5) = (x - √5 i) (x + √5 i)
So, the complete factorization over the complexes is
(x - √5 i)² (x + √5 i)²
The three refers to 3 ten thousands. or 3 x 10,000.
Answer:
The pair (0,3) is not a solution to the equation
Step-by-step explanation:
This can be proved by simply replacing the x and y variables in the equation by the x and y values of the pair, and checking if the equation renders a true statement:
By replacing x and y with their values in the pair (0,3), that is x=0 and y=3, in the equation y = 5 - 2x we get:
3 = 5 - 2 (0)
3 = 5 - 0
3 = 5
which is NOT a true statement.
On the other hand, the other two pairs (2,1) and (1,3) render true statements:
1 = 5 - 2 (2)
1 = 5 - 4
1 = 1
and
3 = 5 - 2 (1)
3 = 5 - 2
3 = 3
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