The product of two consecutive positive integers is greater than their sum by 209. Find these numbers.
2 answers:
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Answer:
Step-by-step explanation:
m∠4 + m∠7 = 180 (Adjacent Angles of a parallelogram)
<u>Given that</u> m∠4 = x + 45, m∠7 = x² + 45
x + 45 + x² + 45 = 180
x² + x + 90 = 180
x² + x = 180 - 90
x² + x = 90
x² + x - 90 = 0
Using mid-term break formula
x² + 10x - 9x - 90 = 0
x(x+10) - 9(x+10) = 0
(x - 9)(x + 10) = 0
<u>Either, </u>
x-9 = 0 <u>OR</u> x+10 = 0
x = 9 <u>OR</u> x = -10
Now,
m < 7 = x² + 45
<u>For x = 9</u>
m < 7 = (9)² + 45
m < 7 = 81 + 45
<h3>m < 7 = 126°</h3><u>For x = -10</u>
m < 7 = (-10)² + 45
m < 7 = 100 + 45
<h3>m < 7 = 145°</h3>Hope this helped!
<h3>~AnonymousHelper1807</h3>