Another math problem Thank You very much.?

Question

What two numbers differ by 10 and have squares that add to 148? Thank You very much.

Answer 1

There are two possible number sets.

12 and 2.
Difference of 10
Squares 144 and 4 add up to 148

-12 and -2
Difference of 10
Squares 144 and 4 add up to 148

Thanks

Answer 2

Let the numbers be x and y, since we know that they differ by 10.

x - y = 10
x^2 + y^2 = 148

(x + y)^2 + (x - y)^2 = x^2 + y^2 + x^2 + y^2
(x + y)^2 + 100 = 2(x^2 + y^2)
(x + y)^2 + 100 = 2*148
(x + y)^2 + 100 = 296
(x + y)^2 = 196
x + y = 14 (Taking square root of both sides)

x + y = 14 ........ (1)
x - y = 10 ......... (2)

Add (1) and (2)

x + y + x - y = 24
2x = 24
x = 12

Put x = 12 in (2)
12 - y = 10
y = 2

The numbers are 12 and 2.


Since the negative values, when squared, will sum up to 148 anyway, -12 and -2 can also be the numbers.

NOTE: Either both numbers must be positve or both numbers must be negative as otherwise, their difference will not be 10.

Answer 3

a - b = 10 and a^2 + b^2 = 148

(a - b)^2 = 100 = a^2 -2ab + b^2 = 148 - 2ab

So, 2ab = 148 - 100 = 48

ab = 24 and the factors of ab are 12 and 2, 8 and 3 and 6 and 4 etc. Out of them 12 and 2 satisfy the condition of differing by 10.

So, we have 12 and 2 as the two numbers.

Answer 4

Let the numbers be x and y
Therefore,it is given that
x-y=10,and
X^2+y^2=148
We know that
(x+y)^2+(x-y)^2=2(x^2+y^20
=>(x+Y)^2+10^2=2*148
=>(x+y)^2=296-100=196
=>x+y=14 [square rooting both sides]
We have now two equations,
x+y=14,and
x-y=10 By solving the equations,we get
x=12 and y=2
Therefore,the numbers are 12 and 2

Answer 5

The second poster is correct, but for the algebraic solution:

let x= 1st number
y= 2nd number

Given:
x-y=10
(x^2) + (y^2)=148

Solution:
x-y=10 [Given]
(x-y)^2 = 10^2
x^2 - 2xy + y^2 = 100

(x^2) + (y^2) = 148 [Given]
-2xy = -48
xy = 24

x= 24/y

* x - y = 10
24/y - y = 10 (by transitivity)
24 - (y^2) = 10y

y=2 and -12
x=12 and -2

[The other posters forgot negative 2 and 12 which also satisfy the equations]

Answer 6

12 and 2

Answer 7

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