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# Algebra

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, 1 month 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,

$$3×\frac{7}{3}+5×\frac{21}{5}+7×\frac{15}{7}$$
$$7+21+15=\boxed{43}.$$ · 1 year, 1 month ago

I sorry. I only know the answer · 1 year, 1 month ago

Ok.Then tell me where I made the mistake in my solution. · 1 year, 1 month ago

Your answer is wrong!! Right answer:71😊 · 1 year, 1 month ago

Then,where I made the mistake.Please show your solution. · 1 year, 1 month ago

Thanks you for your helping.are you sure? · 1 year, 1 month ago