Mathematics: Three numbers, of which the third is equal to 36, form a geometric progression. if 36 is replaced with 20, then the three numbers form an arithmetic progression. find these three numbers.

Three numbers, of which the third is equal to 36,

Ответ:

Rach23s

10.03.2022

Mathematics

The answer is either 4, 12, 36 or 100, 60, 36.

Step-by-step explanation: Let the first two numbers be 'a' and 'b'.

According to the question, a, b and 36 forms a geometric series. So, we have

$\dfrac{b}{a}=\dfrac{36}{b}\\\\\Rightarrow b^2=36a.$

Also, if 36 is replaced by 20, then a, b, 20 will form an arithmetic series. So,

$b-a=20-b\\\\\Rightarrow 2b=20+a\\\\\Rightarrow 2b=20+\dfrac{b^2}{36}\\\\\Rightarrow 72b=720+b^2\\\\\Rightarrow b^2-72b+720\\\\\Rightarrow b^2-60b-12b+720=0\\\\\Rightarrow b(b-60)-12(b-60)=0\\\\\Rightarrow (b-12)(b-60)\\\\\Rightarrow b=12,~~b=60.$

Therefore,

$a=\dfrac{12^2}{36}=4,~~a=\dfrac{60^2}{36}=100.$

Thus, the three numbers are either 4, 12, 36 or 100, 60, 36.

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Ответ:

EllaLovesAnime

06.12.2020

Mathematics

x² + 10x + 24

Step-by-step explanation:

Use foil to multiply them.

x ( x + 4 ) = x² + 4x

6 ( x + 4) = 6x + 24

Combine like terms: x² + 10x + 24

Hope this helps :)

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Three numbers, of which the third is equal to 36, form a geometric progression. if 36 is replaced with 20, then the three numbers form an arithmetic progression. find these three numbers.

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