The sum of two numbers is 72 and their difference is 26. find two numbers?

Mathematics

1 answer:

Archy [21]3 years ago

7 0

9514 1404 393

Answer:

23, 49

Step-by-step explanation:

Let s represent the smaller of the two numbers. Then the larger is s+26, and the sum is ...

s + (s+26) = 72

2s = 72 -26

s = (72 -26)/2 = 23

Then the larger number is

s +26 = 49

The two numbers are 23 and 49.

_____

The reason we wrote the solution this way is to show you that the smaller number is half the difference between the given sum (72) and difference (26). This is the generic solution to a "sum and difference" problem. The smaller number is always half the difference of the give sum and difference. (Similarly, the larger is always half the sum of the given sum and difference.)

That is, the two numbers are always half the sum ± half the difference:

72/2 ± 26/2 = {36+13, 36-13} = {49, 23}

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$W(x)=x^{4}-x^{3}-7x^{2}+x+6$

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Second. Construction a rough graph of $W(x)$

Given that this is a polynomial, then the function is continuous. To graph it we set the roots on the coordinate system. We take the interval:

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Therefore the curve start falling and it goes up and down until $x=3$ and from this point it rises without a bound as shown in the figure below