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If we have \(xy = 7, yz = 3, xz = 5\), then the numerical expression \(3x^2 + 5y^2 + 7z^2\) is equal to:

Note by Mahla Salarmohammadi 1 year, 9 months ago

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\(xy=7\) .....\((1)\) \(yz=3\) .....\((2)\) \(xz=5\) .....\((3)\)

From \((1)\) and \((2)\).

\(x=\frac{7}{y}=\frac{5}{z}\) \(y=\frac{7z}{5}\)

Putting the value of \(y\) in \((3)\).

\(\Rightarrow y^2=\boxed{\frac{21}{5}}\) From \((1)\) and \((2)\). \(y=\frac{3}{z}=\frac{7}{x}\) \(y=3x\) and \(x=\frac{7z}{3}\)

Putting the value of \(y\) in \((1)\).

\(\Rightarrow x^2=\boxed{\frac{7}{3}}\)

Putting the value of \(x\) in \((3)\).

\(\Rightarrow z^2=\boxed{\frac{15}{7}}\)

Now,

\(3×\frac{7}{3}+5×\frac{21}{5}+7×\frac{15}{7}\) \(7+21+15=\boxed{43}.\) – Abhay Kumar · 1 year, 9 months ago

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@Abhay Kumar – I sorry. I only know the answer – Mahla Salarmohammadi · 1 year, 9 months ago

@Mahla Salarmohammadi – Ok.Then tell me where I made the mistake in my solution. – Abhay Kumar · 1 year, 9 months ago

@Abhay Kumar – Your answer is wrong!! Right answer:71😊 – Mahla Salarmohammadi · 1 year, 9 months ago

@Mahla Salarmohammadi – Then,where I made the mistake.Please show your solution. – Abhay Kumar · 1 year, 9 months ago

@Abhay Kumar – Thanks you for your helping.are you sure? – Mahla Salarmohammadi · 1 year, 9 months ago

@Mahla Salarmohammadi – Yes. I am sure. – Abhay Kumar · 1 year, 9 months ago

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TopNewest\(xy=7\) .....\((1)\)

\(yz=3\) .....\((2)\)

\(xz=5\) .....\((3)\)

From \((1)\) and \((2)\).

\(x=\frac{7}{y}=\frac{5}{z}\)

\(y=\frac{7z}{5}\)

Putting the value of \(y\) in \((3)\).

\(\Rightarrow y^2=\boxed{\frac{21}{5}}\)

From \((1)\) and \((2)\).

\(y=\frac{3}{z}=\frac{7}{x}\)

\(y=3x\) and \(x=\frac{7z}{3}\)

Putting the value of \(y\) in \((1)\).

\(\Rightarrow x^2=\boxed{\frac{7}{3}}\)

Putting the value of \(x\) in \((3)\).

\(\Rightarrow z^2=\boxed{\frac{15}{7}}\)

Now,

\(3×\frac{7}{3}+5×\frac{21}{5}+7×\frac{15}{7}\)

\(7+21+15=\boxed{43}.\) – Abhay Kumar · 1 year, 9 months ago

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– Mahla Salarmohammadi · 1 year, 9 months ago

I sorry. I only know the answerLog in to reply

– Abhay Kumar · 1 year, 9 months ago

Ok.Then tell me where I made the mistake in my solution.Log in to reply

– Mahla Salarmohammadi · 1 year, 9 months ago

Your answer is wrong!! Right answer:71😊Log in to reply

– Abhay Kumar · 1 year, 9 months ago

Then,where I made the mistake.Please show your solution.Log in to reply

– Mahla Salarmohammadi · 1 year, 9 months ago

Thanks you for your helping.are you sure?Log in to reply

– Abhay Kumar · 1 year, 9 months ago

Yes. I am sure.Log in to reply