X(x + 3) + x(x - 3) = 2
x^2 + 3x +x^2 - 3x = 2
2x^2 = 2
x^2 = 1
x = +1 and x = -1
answer
x = +1 and x = -1
Answer:
See Explanation Below
Step-by-step explanation:
Given
Required
Prove
To start with; we open the bracket on the left hand side
Reorder
From trigonometry;
So;
becomes
Also from trigonometry;
So,
becomes
Proved
(1) y² + x² = 53
(2) y - x = 5 ⇒ y = x + 5
subtitute (2) to (1)
(x + 5)² + x² = 53 |use (a + b)² = a² + 2ab + b²
x² + 2x·5 + 5² + x² = 53
2x² + 10x + 25 = 53 |subtract 53 from both sides
2x² + 10x - 28 =0 |divide both sides by 2
x² + 5x - 14 = 0
x² - 2x+ 7x - 14 = 0
x(x - 2) + 7(x - 2) = 0
(x - 2)(x + 7) = 0 ⇔ x - 2 = 0 or x + 7 = 0 ⇔ x = 2 or x = -7
subtitute the values of y to (2)
for x = 2, y = 5 + 2 = 7
for x = -7, y = 5 + (-7) = 5 - 2 = 3
Answer: x = 2 and y = 7 or x = -7 and y = 3
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