Using factorization method;
x²+13x+40=0
x²+13+40
Find two numbers that you can add together to give the co-efficient of variable x. (I.e 13 for this question). Also, you'll find two numbers that you can multiply with each other to give you the whole number as an answer. (I.e 40 in this question). The two numbers must be the same (i.e the two numbers that will be added to give the co-efficient of x and the two numbers that will be multiplied to give the whole number must be the same two).
The two numbers are +5 and +8
The equation will therefore be = x²+5x+8x+40
You'll then factorize (I.e use a common factor of both values to bracket them)
x(x+5)+8(x+5)
(x+8)(x+5)
x is therefore (x+8=0) or (x+5=0)
x=(x=0-8) or (x=0-5)
x= -8 or x= -5
Answer:
Y = 21 [Small number].
X = 32 [Big number].
Step-by-step explanation:
Answer:
√11
Step-by-step explanation:
4 = x^2 -7
Add 7 to both sides
11 = x^2
Square root both sides
√11 = x
A) I would make the positive integer x and then form an equation.
x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6
Since the question asks for a positive integer the answer is 7.
B) two positive numbers x and y.
X - y = 3
x^2 + y^2 = 117
Use these simultaneous equations to figure out each number.
Rearrange the first equation
x = y + 3
Then substitute it into the second equation.
(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)
This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.
Use y to find x
x = y + 3
x = 6 + 3
x = 9
So the answers are x = 9 and y = 6.