The product of two numbers is 640 and their arithmetic mean is 26 . find the two numbers
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Step-by-step explanation:
We know that the arithmetic mean between two numbers a and b is AM=
2
a+b
.
Here, it is given that AM=12, therefore,
AM=
2
a+b
⇒12=
2
a+b
⇒a+b=12×2
⇒a+b=24....(1)
It is also given that the product of two numbers a and b is 119, thus,
ab=119.....(2)
Now using equations 1 and 2, consider,
(a−b)
2
=(a+b)
2
−4ab=(24)
2
−(4×119)=576−476=100 implies that
a−b=10.....(3)
Adding equations 1 and 3, we have
(a+a)+(b−b)=24+10
⇒2a=34
⇒a=
2
34
=17
Substitute the value of a in equation 1 as follows:
17+b=24
b=24−17=7
Hence, the numbers are 17 and 7.
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