If ordered pair - where - I satisfy the equation 2x2-3xy-2y2-7-then value of - can be

The correct option is B 4 given equation is 2x^2 3xy 2y^2=7 ⇒ 2x^2 4xy+xy 2y^2 7 ⇒ (x 2y)(2x+y)=7 ⇒ (x 2y) (2x+y)=7× 1 ⇒ differen ...

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Byju's Answer

Standard XII

Mathematics

Using Graph to Find Range of a Function

If ordered pa...

Question

If ordered pair $(α, β)$ where $α, β \in I$ satisfy the equation $2 x^{2} - 3 x y - 2 y^{2} = 7$ ,then value of $α + β$ can be

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Solution

The correct option is B $4$
given equation is
$2 x^{2} - 3 x y - 2 y^{2} = 7$
$\Rightarrow 2 x^{2} - 4 x y + x y - 2 y^{2} - 7$
$\Rightarrow (x - 2 y) (2 x + y) = 7$
$\Rightarrow (x - 2 y) (2 x + y) = 7 \times 1$

$\Rightarrow$ different possible condition by comparing both side can be
$x - 2 y = 7 - - - (1)$ and
$2 x + y = 1 - - - (2)$

Solving $(1)$ and $(2)$

$- 2 y = 7 - - - - (1) \times 1 2 x + y = 1 - - - (2) \times 2________x - 2 y = 7 4 x + 2 y = 2 + + +5 x = 9 x = \frac{9}{5}$

Similarly,
$y = \frac{- 13}{5}$

$x - 2 y = 1 - - - - (3) \times 1 2 x + y = 7 - - - (4) \times 2_x - 2 y = 1 4 x + 2 y = 14 +_________5 x = 15 x = 3$

Similarly
$y = 1$
So possible value of $(α, β)$ , i.e, $(x, y)$ is
$(\frac{9}{5}, \frac{- 13}{5})$ and $(3, 1)$
$∴ α + β = 4$ or $\frac{4}{5}$
Answer $(B) 4$

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If ordered pair (α,β) where α,β∈I satisfy the equation 2x2−3xy−2y2=7,then value of α+β can be

If ordered pair $(α, β)$ where $α, β \in I$ satisfy the equation $2 x^{2} - 3 x y - 2 y^{2} = 7$ ,then value of $α + β$ can be