If x+y = 5 and xy = 6 , find (x³+y³)

x²+y²=13

Step-by-step explanation:

x+y=5

now,

squaring both side

(x+y)²=5²

x²+2.x.y+y²=25

x²+y²+2×6=25 (putting value of xy=6)

x²+y²=25-12

x²+y²=13

hope it helps.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions