Find $a,b,k$: Solving Equations

In summary, the process for solving equations involves isolating the variable, using inverse operations and simplifying. For equations with multiple variables, substitution or elimination can be used. Equations with fractions or decimals can also be solved using the same process. To check if the solution is correct, it can be plugged back into the original equation or graphed. There are also special rules, such as the distributive property and the zero product property, that can be applied when solving equations.
  • #1
Albert1
1,221
0
given :

$a-b=k---(1)$

$a^2-b^2=70---(2)$

where $k\in N$ , and $0<b<1$

please find the values of $a,b ,k$
 
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  • #2
Albert said:
given :

$a-b=k---(1)$

$a^2-b^2=70---(2)$

where $k\in N$ , and $0<b<1$

please find the values of $a,b ,k$

from the second equation as $0 < b < 1$ so $70<a^2<71$ hence the value of taking integers between 8 and 9
so we have
$8 < a < 9$ and k is integer part of a so k = 8
$a = 8 + b$
so we get
$a^2-b^2 = (8+b)^2-b^2 = 64 + 16b= 70$ or $b = \dfrac{3}{8}$
hence $k=8,b= \dfrac{3}{8}, a = 8\dfrac{3}{8}$
 

FAQ: Find $a,b,k$: Solving Equations

What is the process for solving equations?

The general process for solving equations involves isolating the variable you are solving for on one side of the equation and simplifying the other side. This can be done by using inverse operations, combining like terms, and applying the order of operations. The goal is to end up with the variable by itself on one side of the equation.

How do you solve equations with multiple variables?

To solve equations with multiple variables, you will need to use substitution or elimination. Substitution involves solving for one variable in terms of the other and then plugging that into the other equation. Elimination involves adding or subtracting equations to eliminate one variable and then solving for the remaining variable.

Can I solve equations with fractions or decimals?

Yes, equations with fractions or decimals can be solved using the same process as equations with whole numbers. It is important to simplify fractions and convert decimals to fractions before beginning the solving process.

How do I know if my solution is correct?

To check if your solution is correct, you can plug it back into the original equation and see if the equation is true. If the equation is true, then your solution is correct. You can also graph the equation and see if the solution is the point where the graph intersects the x-axis.

Are there any special rules for solving equations?

Yes, there are a few special rules for solving equations. These include the distributive property, which allows you to multiply a number or expression to every term inside parentheses, and the zero product property, which states that if the product of two numbers or expressions is equal to zero, then one or both of the numbers or expressions must be equal to zero.

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