Question 3

Find the value of $$\sqrt{(2x-5)^{2}}+2\sqrt{(x-1)^{2}}$$, if $$1<x<2$$

Solution

Since, $$1<x<2$$

$$\sqrt{\left(2x-5\right)^2}=5-2x$$ (as value in square root should be positive)

$$=$$> $$\sqrt{\left(2x-5\right)^2}+2\sqrt{\left(x-1\right)^2}=5-2x+2\left(x-1\right)=5-2x+2x-2=3$$

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