What's 5 - the square root of x + 10 = the square root of 7 - x

1 answer:

3 0

$\bf 5-\sqrt{x+10}=\sqrt{7-x}\impliedby \textit{squaring both sides}
\\\\\\
(5-\sqrt{x+10})^2=(\sqrt{7-x})^2
\\\\\\
(5^2)-10\sqrt{x+10}+(x+10)=7-x
\\\\\\
35-10\sqrt{x+10}+x=7-x\implies 28-10\sqrt{x+10}+2x=0
\\\\\\
2x+28=10\sqrt{x+10}\implies x+14=5\sqrt{x+10}\impliedby 
\begin{array}{llll}
squaring\ both\\
sides\ again
\end{array}
\\\\\\
$

$\bf (x^2)+28x+(14^2)=5^2(x+10)\implies x^2+28x+196=25x+250
\\\\\\
\begin{array}{lcclll}
x^2&+3x&-54&=0\\
&\uparrow &\uparrow \\
&-6+9&-6\cdot 9
\end{array} \implies (x+9)(x-6)=0\implies 
\begin{cases}
x+9=0\\
\boxed{x=-9}\\
-----\\
x-6=0\\
\boxed{x=6}
\end{cases}$

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Omg ty for the help<br><br>is this the correct way to solve for x?

Degger [83]

Answer:

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Step-by-step explanation:

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Yes! That's exactly right.

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2 years ago

Select all the expressions that are equivalent to −5/6 / -1/3

Sindrei [870]

Step-by-step explanation:

We need to find an expression for $\dfrac{\dfrac{-5}{6}}{\dfrac{-1}{3}}$ .

We can solve it as follows.

We know that,

$\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\times \dfrac{d}{c}$

So,

$\dfrac{\dfrac{-5}{6}}{\dfrac{-1}{3}}=\dfrac{-5}{6}\times -3\\\\=\dfrac{5}{2}$

$=2\dfrac{1}{2}$

Hence, this is the required solution.

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2 years ago

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11Alexandr11 [23.1K]

Solve for x:
x^9 = n x

Subtract n x from both sides:
x^9 - n x = 0

Factor x and constant terms from the left hand side:
-x (n - x^8) = 0

Multiply both sides by -1:
x (n - x^8) = 0

Split into two equations:
x = 0 or n - x^8 = 0

Subtract n from both sides:
x = 0 or -x^8 = -n

Multiply both sides by -1:
x = 0 or x^8 = n

Taking 8^th roots gives n^(1/8) times the 8^th roots of unity:
Answer: x = 0 or x = -n^(1/8) or x = -i n^(1/8) or x = i n^(1/8) or x = n^(1/8) or x = -(-1)^(1/4) n^(1/8) or x = (-1)^(1/4) n^(1/8) or x = -(-1)^(3/4) n^(1/8) or x = (-1)^(3/4) n^(1/8)

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3 years ago

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Svetlanka [38]

Answer:

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