25 points
if a-b=7
and
a×b=18
find the value of a+b
with full explanation
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★ QUADRATIC RESOLUTION ★
Given relationship :
a - b = 7 ... ( i )
a × b = 18 or , b = 18/ a
Substituting the value in equation ( i )
it's resolved into a quadratic equation :
a - b = 7
a - 18/ a = 7
a² - 18 / a = 7
a² - 18 = 7a
a² - 18 - 7a = 0
a² - 7a - 18 = 0
a² - 9a + 2a - 18 = 0
a (a - 9 ) + 2 ( a - 9 ) = 0
a - 9 ( a + 2 ) = 0
Hence , a = 9 , -2
If a = 9 , b = 2 : a + b = 11
If a = -2 , b = -9 : a + b = -11
Literally , take positive case in consideration first ,
Therefore , a + b = 11
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
Given relationship :
a - b = 7 ... ( i )
a × b = 18 or , b = 18/ a
Substituting the value in equation ( i )
it's resolved into a quadratic equation :
a - b = 7
a - 18/ a = 7
a² - 18 / a = 7
a² - 18 = 7a
a² - 18 - 7a = 0
a² - 7a - 18 = 0
a² - 9a + 2a - 18 = 0
a (a - 9 ) + 2 ( a - 9 ) = 0
a - 9 ( a + 2 ) = 0
Hence , a = 9 , -2
If a = 9 , b = 2 : a + b = 11
If a = -2 , b = -9 : a + b = -11
Literally , take positive case in consideration first ,
Therefore , a + b = 11
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
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