If the equation x2 + y2 -10x + 21 = 0 has real roots x = a and y=β then

Question

If the equation x2 + y2 -10x + 21 = 0 has real roots x = a and y=β then (A) 3 le x le7 (B) 3 le y le7 (C) -2 le y le2 (D) -2 le x le2

Tardigrade Admin · Accepted Answer

x2-10x+(y2+21)=0 for real roots of x, D ge0 100-4(y2+21) ge0 ⇒ y2 le4 ⇒ -2 le y le2 (C) also, y2=-x2+10x-21 for real roots of y, -x2+10x-21 ge0 ⇒ (x-7)(x-3) le0 3 le x le7 (A)

Q. If the equation $x^{2} + y^{2} - 10 x + 21 = 0$ has real roots $x = a$ and $y = β$ then

$3 \leq x \leq 7$

$3 \leq y \leq 7$

$- 2 \leq y \leq 2$

$- 2 \leq x \leq 2$

Q. If the equation x2+y2−10x+21=0 has real roots x=a and y=β then

3≤x≤7

3≤y≤7

−2≤y≤2

−2≤x≤2

x2−10x+(y2+21)=0 for real roots of x,D≥0 100−4(y2+21)≥0 ⇒y2≤4 ⇒−2≤y≤2(C) also, y2=−x2+10x−21 for real roots of y, −x2+10x−21≥0 ⇒(x−7)(x−3)≤0 3≤x≤7(A)

Q. If the equation $x^{2} + y^{2} - 10 x + 21 = 0$ has real roots $x = a$ and $y = β$ then

$3 \leq x \leq 7$

$3 \leq y \leq 7$

$- 2 \leq y \leq 2$

$- 2 \leq x \leq 2$