# Find all possible solutions of c and d

• MHB
• albert391212
In summary, to find all possible values of c and d where a = 70, b = 61, and a^2 + b^2 + c^2 = d^2, we can use the equation (d+c)(d-c) = 8621 and solve for c and d by choosing all pairs of numbers that multiply together to equal 8621. The two sets of solutions are (4311,4310) and (135,98).
albert391212
$$\displaystyle if : a^2 + b^2 +c^2 = d^2$$
where a,b c and d both are positive integers
if a=70 ,b=61
find all posible values of c and d

we have $70^2 + 61^2 + c^2 = d^2$
or $4900 +3721 + c^2 -= d^2$
or $d^2-c^2 = 8621$
or ($d+c)(d-c) = 8621$
to solve the same you can put 8621 as product of 2 numbers (one case 8621 * 1$equiate one to d +c and another to d- c and solve for c and d. by choosing all pair of numbers fot erach pair one set of c d can be obtained kaliprasad said: we have$70^2 + 61^2 + c^2 = d^2$or$4900 +3721 + c^2 -= d^2$or$d^2-c^2 = 8621$or ($d+c)(d-c) = 8621$to solve the same you can put 8621 as product of 2 numbers (one case 8621 * 1$ equiate one to d +c and another to d- c and solve for c and d. by choosing all pair of numbers fot erach pair one set of c d can be obtained
(d+c)(d-c)=8621
the only solution is
d=4321
c=4320

(d+c)(d-c)=8621=(8621)(1)=(233)(37)
the solution is
(d,c)=(4321,4320),(135,98)#

we have $70^2 + 61^2 + c^2 = d^2$
or $4900 +3721 + c^2 -= d^2$
or $d^2-c^2 = 8621$
or ($d+c)(d-c) = 8621$
to solve the same you can put 8621 as product of 2 numbers (one case 8621 * 1\$ equiate one to d +c and another to d- c and solve for c and d. by choosing all pair of numbers fot erach pair one set of c d can be obtained

Albert

Albert391212 said:
(d+c)(d-c)=8621=(8621)(1)=(233)(37)
the solution is
(d,c)=(4321,4320),(135,98)#
(d+c)(d-c)=8621=(8621)(1)=(233)(37)
the solution is
(d,c)=(4311,4310),(135,98)#
sorry again
I have a poor calculation
we have two sets of solution
d=135 or 4311
c=98 or 4310
(d,c)=(4311,4310),(135,98)#

## 1. What does "find all possible solutions of c and d" mean?

"Find all possible solutions of c and d" means to determine all of the potential values for the variables c and d that satisfy a given equation or set of conditions.

## 2. Why is it important to find all possible solutions of c and d?

It is important to find all possible solutions of c and d in order to fully understand the problem at hand and to ensure that no potential solutions are overlooked. This can also help to identify patterns and relationships between variables.

## 3. How do you find all possible solutions of c and d?

To find all possible solutions of c and d, you can use algebraic methods such as substitution or elimination, or you can use graphical methods such as plotting points or using a graphing calculator.

## 4. What if there are an infinite number of solutions for c and d?

If there are an infinite number of solutions for c and d, you can still find the general solution by expressing the solutions in terms of a variable or using a pattern to represent the solutions.

## 5. Can there be more than one solution for c and d?

Yes, there can be more than one solution for c and d. In fact, most equations have multiple solutions. It is important to find all possible solutions in order to fully understand the problem and to determine the most appropriate solution for a given situation.

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