a^2-b^2 = (a-b)(a+b) = 150. For (a-b) = 5. (a+b) = 150/(a-b) = 150/5 = 30.
( a - b ) ( a + b ) = 150
5 ( a + b ) = 150
a + b = 30
a+ b = 150/5
= 30
a² - b² = 150
a - b = 5 sincea² - b² = ( a - b ) * ( a + b )
150 = 5 * (?)thena + b = 150/5 = 30✔
The values of a and b are 17.5 and 12.5 respectively and so 17.5+12.5 = 30
a - b = 5
Factor
(a - b)(a + b) = 150
5(a + b) = 150
a-b=5 ==> a=5+b
Now: a^2-b^2=150 ===> (5+b)^2-b^2=150.
You can take it from there.
Remember the factoring of a difference of squares:
a² - b² = (a - b)(a + b)
In your case:
150 = 5(a + b)
a + b = 150/5
Note: It's not necessary to find the specific values of a and b, but you could:
--------------
2a = 35
a = 17½
b = 12½
Double-check:
a² - b²
= 17.5² - 12.5²
= 306.25 - 156.25
= 150
a - b
= 17.5 - 12.5
= 5
a + b
= 17.5 + 12.5
Answer:
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Answers & Comments
a^2-b^2 = (a-b)(a+b) = 150. For (a-b) = 5. (a+b) = 150/(a-b) = 150/5 = 30.
( a - b ) ( a + b ) = 150
5 ( a + b ) = 150
a + b = 30
a+ b = 150/5
= 30
a² - b² = 150
a - b = 5 sincea² - b² = ( a - b ) * ( a + b )
150 = 5 * (?)thena + b = 150/5 = 30✔
The values of a and b are 17.5 and 12.5 respectively and so 17.5+12.5 = 30
a² - b² = 150
a - b = 5
a + b = 30
Factor
(a - b)(a + b) = 150
5(a + b) = 150
a + b = 30
a-b=5 ==> a=5+b
Now: a^2-b^2=150 ===> (5+b)^2-b^2=150.
You can take it from there.
Remember the factoring of a difference of squares:
a² - b² = (a - b)(a + b)
In your case:
150 = 5(a + b)
a + b = 150/5
a + b = 30
Note: It's not necessary to find the specific values of a and b, but you could:
a - b = 5
a + b = 30
--------------
2a = 35
a = 17½
b = 12½
Double-check:
a² - b²
= 17.5² - 12.5²
= 306.25 - 156.25
= 150
a - b
= 17.5 - 12.5
= 5
a + b
= 17.5 + 12.5
= 30
Answer:
a + b = 30