The minimum value of y in the equation y = x\(^2\) - 6x + 8 is
8
3
7
-1
Correct answer is D
y = x\(^2\) - 6x + 8
\(\frac{dy}{dx}\) = 2x - 6
\(\frac{dy}{dx}\) = 0
2x - 6 = 0
x = 3
\(\therefore\) y = 3\(^2\) - 6(3) + 8
= 9 - 18 + 8
= -1
Simplify \(\frac{x^2 - y^2}{2x^2 + xy - y^2}\)
\(\frac{x + y}{2x + y}\)
\(\frac{x + y}{2x - y}\)
\(\frac{x - y}{2x - y}\)
\(\frac{x - y}{2x + y}\)
Correct answer is C
\(\frac{x^{2} - y^{2}}{2x^{2} + xy - y^{2}}\)
\(2x^{2} + xy - y^{2} = 2x^{2} - xy + 2xy - y^{2}\)
= \(x(2x - y) + y(2x - y) \)
= \((x + y)(2x - y)\)
\(\frac{x^{2} - y^{2}}{2x^{2} + xy - y^{2}} = \frac{(x + y)(x - y)}{(x + y)(2x - y)}\)
= \(\frac{x - y}{2x - y}\)
Solve the inequality x - 1 > 4(x + 2)
x > -3
x < -3
2 < x < 3
-3 < x < -2
Correct answer is B
x - 1 > 4(x + 2) = x - 1 > 4x + 8 4x + 8 < x - 1 = 4x - x < -1 -8 = 3x < -9 ∴ x < -3
An (n - 2)2 sided figure has n diagonals. Find the number n diagonals for 25-sided figure
7
8
9
10
Correct answer is A
(n - 2)2 = 25
n - 2 = 25 = 5
n = 5 + 2
= 7
Find the values of y which satisfy the simultaneous equations x + y = 5, x2 - 2y2 = 1
-12, -2
-12, 12
-12, +2
2, -2
Correct answer is C
x + y = 5.......(i) x2 - 2y2 = 1.......(ii) x = 5 - y.........(iii) Subst. for x in eqn.(ii) = (5 - y)2 - 2y2 = 1 25- 10y + y2 - 2y2 = 1 25 - 1 = y2 + 10y y2 + 10y2 - 24 = 0 (y + 12)(y - 2) = 0 Then Either y + 12 = 0 or y - 2 = 0 = (-12, +2)