Answer:
The extraneous solution is 4.
Step-by-step explanation:
First, let us calculate the value of 'x' without squaring both side of the expression. This is illustrated below:
-5 = 3x - 7
Collect like terms
-5 + 7 = 3x
2 = 3x
Divide both side by 3
x = 2/3.
Now, let us calculate the value of 'x' by squaring both side of the expression. This is illustrated below:
(-5)^2 = (3x - 7)^2
25 = (3x - 7)(3x - 7)
25 = 9x^2 - 21x - 21x + 49
9x^2 - 42x + 49 - 25 = 0
9x^2 - 42x + 24 = 0
Solving by factorisation:
Multiply the first term i.e 9x^2 and 3rd term i.e 24 together. The result is 216x^2.
Next, we shall obtain two factors of 216x^2 such that when we add them together, it will give the 2nd term i.e -42x in the equation. These factors are: -6x and -36x
Now we can write the above equation as:
9x^2 - 42x + 24 = 0
9x^2 - 6x - 36x + 24 = 0
3x(3x - 2) - 12(3x - 2) = 0
(3x - 12)(3x - 2) = 0
3x - 12 = 0 or 3x - 2 = 0
3x = 12 or 3x = 2
x = 12/3 or x = 2/3
x = 4 or 2/3.
We can see that when we solve the question without squaring both side, the value of x is 2/3. But when we solve by squaring both side, the value of x are 4 and 2/3.
Therefore, the extraneous solution to the question is 4.
ANSWER
83
EXPLANATION
This method makes use of a system of equations
Let x be the tens-place digit
Let y be the ones-place digit
(therefore, x and y are positive integers between 0 and 9 inclusive as they represent digits)
Then this two digit number is 10x + y
"Multiplying it by itself gives 6889" implies
(10x + y)(10x + y) = 6889
or just
(10x + y)² = 6889
Square root both sides.
Note that √(10x + y)² = 10x + y since x and y are positive and √6889 is 83
10x + y = 83
Now use the other information to make another equation
The sum of its digits is 11 so
x + y = 11
We have a system of equations as x and y must satisfy both equations for the question conditions to be met:
10x + y = 83 ... (I)
x + y = 11 ... (II)
This can be solved using elimination. Multiplying (II) by -1 to aim to get rid of y, we get
10x + y = 83 ... (I)
- x - y = -11 ... (II)
Adding the two equations, we get
(10x - x) + (y - y) = (83 - 11)
which is
9x = 72
Divide both sides by 9 to get
x = 8
This is the tens digit.
Can use x + y = 11 ... (II) to figure out value of y,
x + y = 11
⇒ y = 11 - x
⇒ y = 11 - 8
⇒ y = 3
x = 8 and y = 3
x is the tens-place digit
y is the ones-place digit
The number is 83
10000+200= 10200
10200+204=10404
10404+208= 10612
10612+212= 10824
10824+216= 11 040
11040+220= 11260
Answer:
5^5
Step-by-step explanation:
25 is five to the second power, and when you multiply exponents, you add them together. So you have 5^3 x 5^2 which will be 5^5.