If (a,b) is positive integral solution of the equation $7 x^{2} - 2 x y + 3 y^{2} = 27$ , then max. b + min. a =

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Solution

The correct option is B
3

$7 x^{2} - 2 x y + 3 y^{2} - 27 = 0$

$\Rightarrow$ $x = \frac{(2 y \pm \sqrt{4 y^{2} - 28 (3 y^{2} - 27)})}{14}$

$\Rightarrow$ $x = \frac{(y \pm \sqrt{189 - 20 y^{2}})}{7}$

$x, y ϵ N$ $\Rightarrow$ $y^{2}$ < $\frac{189}{20}$ $\Rightarrow$ $y = 1 o r 2 .$

$y = 1$ $\Rightarrow$ $x = 2 a n d y = 2, x \notin N$

$∴$ Only solution is x = 2 , y =1 i.e., a=2 , b=1

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If (a,b) is positive integral solution of the equation 7x2−2xy+3y2=27 , then max. b + min. a =

The correct option is B 3 7x2−2xy+3y2−27=0 ⇒ x=(2y±√4y2−28(3y2−27))14 ⇒ x=(y±√189−20y2)7 x,y ϵ N ⇒ y2 < 18920 ⇒ y=1or2. y=1 ⇒x=2 and y=2,x ∉ N ∴ Only solution is x = 2 , y =1 i.e., a=2 , b=1

If (a,b) is positive integral solution of the equation $7 x^{2} - 2 x y + 3 y^{2} = 27$ , then max. b + min. a =