GATE 2017 EE (EE2) – Question 30

Engineering Mathematics · Linear Algebra: Systems of linear equations · 1 mark · Numerical answer

Let $y^2-2y+1=x$ and $\sqrt x+y=5$. Find $x+\sqrt y$, to three decimal places.

Show answer and explanation

Correct answer: 5.7 to 5.8

Explanation

The first equation is $x=(y-1)^2$, so $\sqrt x=|y-1|$. Hence $|y-1|+y=5$.

For y≥1 this becomes 2y−1=5, giving y=3 and x=4. For y<1 the left side is identically 1 and cannot equal 5.

The unique valid result is $4+\sqrt3=5.7320508\ldots$, or **5.732**.

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