(i) 2a+2b = 2(0)+2(-1) = 0-2=-2 [putting a=0,b=-1]
(ii) 2a2+b2+1 = 2(0)2+(-1)2+1 = 2×0+1+1 = 0+2 = 2 [putting a=0,b=-1]
(iii) 2a2b+2ab2+ab = 2(0)2(-1)+2(0)(-1)2+(0)(-1) = 0+0+0 = 0 [putting a=0,b=-1]
(iv) a2+ab+2 = (0)2+(0)(-1)+2 = 2 [putting a = 0,b=-1]
If \( x, y \) are two positive integers such that \( x + y = 20 \) and the maximum value of \( x^3 y \) is \( k \) at \( x = a, y = \beta \), then \( \frac{k}{\alpha^2 \beta^2} = ? \)
Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.
(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.
(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30