If the point $(α, α^{2})$ lies on or inside the triangle formed by the lines $x^{2} y + x y^{2} - 2 x y = 0,$ then the largest possible value of $α$ is

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Solution

$x^{2} y + x y^{2} - 2 x y = 0$
$\Rightarrow (x y) (x + y) - 2 x y = 0$
$\Rightarrow x y (x + y - 2) = 0$

Point lies on or inside the triangle formed by the lines
$x = 0, y = 0 and x + y = 2$
Required conditions are
$(i) α \geq 0 (i i) α^{2} \geq 0$
$(i i i) α + α^{2} - 2 \leq 0$

$\Rightarrow α \in [0, 1]$

So, largest value of $α = 1$

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If the point (α,α2) lies on or inside the triangle formed by the lines x2y+xy2−2xy=0, then the largest possible value of α is

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If the point $(α, α^{2})$ lies on or inside the triangle formed by the lines $x^{2} y + x y^{2} - 2 x y = 0,$ then the largest possible value of $α$ is