# 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
2 years, 7 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

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

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,

$$3×\frac{7}{3}+5×\frac{21}{5}+7×\frac{15}{7}$$
$$7+21+15=\boxed{43}.$$

- 2 years, 7 months ago

I sorry. I only know the answer

- 2 years, 6 months ago

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

- 2 years, 6 months ago

- 2 years, 6 months ago

- 2 years, 6 months ago

Thanks you for your helping.are you sure?

- 2 years, 7 months ago

Yes. I am sure.

- 2 years, 6 months ago