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frez [133]
2 years ago
9

The only way to stay at an appropriate weight is to balance food intake with calories burned.

Health
1 answer:
NARA [144]2 years ago
5 0

Answer:

true

Explanation:

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If 2^x=3^y=12^z, show that 1÷z=1÷y+2÷x.....​
Ostrovityanka [42]

Answer:

Proof of \dfrac{1}{z}}=\dfrac{1}{y}+\dfrac{2}{x}  is shown below.

Explanation:

The given equation is

2^x=3^y=12^z

To prove : \dfrac{1}{z}=\dfrac{1}{y}+\dfrac{2}{x}

Proof : Let as assume,

2^x=3^y=12^z=k

2^x=k\Rightarrow 2=k^{\frac{1}{x}}    ...(1)

3^y=k\Rightarrow 3=k^{\frac{1}{y}}      ...(2)

12^z=k\Rightarrow 12=k^{\frac{1}{z}}    ...(3)

We know that

12=2\times 2\times 3

12=(2)^2\times 3

Using (1), (2) and (3), we get

k^{\frac{1}{z}}=(k^{\frac{1}{x}})^2\times k^{\frac{1}{y}}

k^{\frac{1}{z}}=k^{\frac{2}{x}}\times k^{\frac{1}{y}}

k^{\frac{1}{z}}=k^{\frac{2}{x}+\frac{1}{y}}

On comparing both sides, we get

\dfrac{1}{z}}=\dfrac{2}{x}+\dfrac{1}{y}

\dfrac{1}{z}}=\dfrac{1}{y}+\dfrac{2}{x}

Hence proved.

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