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Question Number 213430 by hardmath last updated on 05/Nov/24

$$\mathrm{x},\mathrm{y},\mathrm{z}\in \mathbb{R}$$$$\{\begin{array}{l}\mathrm{x}+\left[\mathrm{y}\right]+\left\{\mathrm{z}\right\}=9,4\\ \left[\mathrm{x}\right]+\left\{\mathrm{y}\right\}+\mathrm{z}=11,3\\ \left\{\mathrm{x}\right\}+\mathrm{y}+\left[\mathrm{z}\right]=10,5\end{array}\mathrm{find}:\mathbf{x}=?$$

Answered by A5T last updated on 05/Nov/24

$$\left(i\right)-\left(ii\right):\left\{x\right\}+\left[y\right]-\left\{y\right\}-\left[z\right]=-1.9...\left(iv\right)$$$$\left(iv\right)-\left(iii\right)\Rightarrow \left[y\right]-\left\{y\right\}-y-2\left[z\right]=-12.4$$$$\Rightarrow \left\{y\right\}+\left[z\right]=6.2;\Rightarrow \left[z\right]=6\Rightarrow \left\{y\right\}=0.2$$$$\left(iii\right)\Rightarrow \left\{x\right\}+\left[y\right]+\left\{y\right\}=4.5\Rightarrow \left\{x\right\}+\left[y\right]=4.3$$$$\Rightarrow \left[y\right]=4\Rightarrow \left\{x\right\}=0.3$$$$\left(i\right)\Rightarrow \left[x\right]+0.3+4+\left\{z\right\}=9.4\Rightarrow \left[x\right]+\left\{z\right\}=5.1$$$$\Rightarrow \left[x\right]=5;\left\{z\right\}=0.1\Rightarrow x=5.3\Rightarrow (x,y,z)=(5.3,4.2,6.1)$$

Commented by hardmath last updated on 06/Nov/24

$$\mathrm{than}\mathrm{kyou}\mathrm{dear}\mathrm{professor}$$$$\mathrm{Answer}:5.3,4.2,6.1\mathrm{hov}?$$

Commented by hardmath last updated on 06/Nov/24

$$$$Does it pay when you put it in place?

Commented by A5T last updated on 06/Nov/24

$$x=5.3$$

Commented by hardmath last updated on 06/Nov/24

$$$$Does it pay when you put it in place?

Commented by A5T last updated on 06/Nov/24

$$I{don}^{\prime }treallyunderstandwhatyoumeanbythat$$$$question.$$

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