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Thepotemich [5.8K]
3 years ago
10

Step by step how to solve this equation by completing the square x^2-16x+-60

Mathematics
1 answer:
anygoal [31]3 years ago
5 0

Answer:

Step-by-step explanation:

x^2-16x+60

(x-6)(x-10) factor the equation

x-6=0

x=6

x-10=0

x=10

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The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b.
denis-greek [22]
\mathrm{gcd}(a,b)=9\implies9\mid a\text{ and }9\mid b\implies9\mid a+b

which means there is some integer k for which a+b=9k.


Because 9\mid a and 9\mid b, there are integers n_1,n_2 such that a=9n_1 and b=9n_2, and


\mathrm{lcm}(a,b)=\mathrm{lcm}(9n_1,9n_2)=9\mathrm{lcm}(n_1,n_2)=378\implies\mathrm{lcm}(n_1,n_2)=42

We have 42=2\cdot3\cdot7, which means there are four possible choices of n_1,n_2:

1, 42
2, 21
3, 14
6, 7

which is to say there are also four corresponding choices for a,b:

9, 378
18, 189
27, 126
54, 63

whose sums are:

387
207
153
117

So the least possible value of a+b is 117.
6 0
3 years ago
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