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Engineering Mathematics

Review of Functions

Let x and y b...

Question

Let x and y be integers satisfying the following equations

$2 x^{2} + y^{2} = 34$ and

$x + 2 y = 11$

The value of (x + y) is _____ .
7

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Solution

The correct option is A 7
$2 x^{2} + y^{2} = 34$ ...(i)

and $x + 2 y = 11$ ...(ii)

Solving (i) & (ii)

$2 x^{2} + {(\frac{11 - x}{2})}^{2} = 34$

$\Rightarrow 8 x^{2} + 121 + x^{2} - 22 x = 136$

$\Rightarrow 9 x^{2} - 22 x - 15 = 0$

x = $\frac{22 \pm 32}{18} = 3, \frac{- 10}{18}$
Given that x and y are integers. So x=3

From (ii), y = 4

Hence value of (x + y) = 3 + 4 = 7

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Let x and y be integers satisfying the following equations 2x2+y2=34 and x+2y=11 The value of (x + y) is _____ .7

The correct option is A 7 2x2+y2=34 ...(i) and x+2y=11 ...(ii) Solving (i) & (ii) 2x2+(11−x2)2=34 ⇒8x2+121+x2−22x=136 ⇒9x2−22x−15=0 x = 22±3218=3,−1018 Given that x and y are integers. So x=3 From (ii), y = 4 Hence value of (x + y) = 3 + 4 = 7

Let x and y be integers satisfying the following equations

$2 x^{2} + y^{2} = 34$ and

$x + 2 y = 11$

The value of (x + y) is _____ .
7