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1 year ago

Solve and simplify: x(x - 1) = 121 – x

Mathematics

2 answers:

vaieri [72.5K]1 year ago

4 0

Answer:

$\boxed{\bold{x \ = \ 11 \ or \ x \ = \ -11}}$

Explanation:

$\bold{x(x \ - \ 1) \ = \ 121 \ - \ x}$

Simplify both sides of the equation

x² − x = −x + 121

Add x to both sides

x² − x + x = −x + 121 + x

x² = 121

Take square root

x = ± √121

x = 11 or x = −11

GuDViN [60]1 year ago

3 0

Answer:

$x=11$

Step-by-step explanation:

$x(x-1)=121-x\\\\x^2-x=121-x\\\\x^2=121\\\\x=\sqrt{121}\\\\x=11$

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musickatia [10]

(a) Suppose $h_n=r^n$ is a solution for this recurrence, with $r\neq0$ . Then

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So we expect a general solution of the form

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With $h_0=0,h_1=1,h_2=1,h_3=2$ , we get four equations in four unknowns:

$\begin{cases}c_1+c_2=0\\-c_1+2c_2+2c_3+2c_4=1\\c_1+4c_2+8c_3+16c_4=1\\-c_1+8c_2+24c_3+72c_4=2\end{cases}\implies c_1=-\dfrac8{27},c_2=\dfrac8{27},c_3=\dfrac7{72},c_4=-\dfrac1{24}$

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$\displaystyle\sum_{n\ge4}h_nx^n=5\sum_{n\ge4}h_{n-1}x^n-6\sum_{n\ge4}h_{n-2}x^n-4\sum_{n\ge4}h_{n-3}x^n+8\sum_{n\ge4}h_{n-4}x^n$
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Solve and simplify: x(x - 1) = 121 – x​

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