the difference of two figures is 8. thediff of two squares is 400. tell what it is?

these two figures are 21 and 29.there difference is 8.and there squares are 441 and 841 respectively ,and the difference of squares is 400.

The equation can be solved easily, as long as you remember to substitute at the right time.

We know:

x^2 - y^2 =400

x - y = 8

x^2 - y^2 = 400 Factor the squared terms

(x + y) ( x - y) = 400

We know from the first statements that x-y = 8, so substitute the 8 into the above equation:

8( x + y) = 400 Divide by both side by 8

x + y = 50 Add this equation to the one we know:

x + y = 50

+x - y = 8

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2x = 58 so x = 29 Now plug the value of x into the second equation we know:

x - y = 8 29 - 8 = y therefore , y = 21

x = 29 and y = 21

Also, you can plug both values into the second equation, and you will see it works.

The best way to answer this question is to use algebra. Call the two numbers "a" and "b":

a-b=8

a^2 - b^2 = 400

You can solve these unknowns by the following method:

Rearrange the first equation to solve for "a":

a=8+b

Substitute into the second equation:

(8+b)^2 - b^2=400

Expand:

64 + 16b +b^2 -b^2 =400

Simplify:

64 +16b =400

Subtract 64 from each side:

16b=336

Divide both sides by 16:

b=21

Substitute into the modified first equation:

a=8+21

a= 29

Check the equations to make sure:

29 - 21= 8 good

29^2 - 21^2 = 400 good

Ta da!! a=29 and b=21

x-y=8

x=y+8

x^2-y^2=400

(y+8)^2-y^2=400

(y+8)(y+8)-y^2=400

y^2+8y+8y+64-y^2=400

y^2-y^2=0 SO

8y+8y+64=400

16y=336

y=21

Substitue y into original equation.

x-21=8

x=29

The two figures are 21 and 29. Their difference is 8.

29-21=8. The difference of the squares is 400.

841-441=400.

29 and 21

21 and 29

Let the figures be x and y.

We have the equations

x-y=8

X^2-y^2=400

now it is very simple

x^2-y^2=(x+y)(x-y)=400

therefore x+y=400/8=50

y=50-x

x=y+8=50-x+8

2x=58

x=29

y=21

verification

x-y=8 ok

x^2-Y^2=841-441=400 ok

Let the two numbers be a and b.

As per given condition:

a-b=8..............(1) and a^2-b^2=400...................(2)

a^2-b^2=400

(a+b)*(a-b)=400

(a+b)*8=400 .........................from equation (1)

.:.(a+b)=400/8=50 .................equation(3)

from equation(1) and (3)

a+b=50

a-b=8

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2a=58

.:.a=29

after substituting a=29 in equation(3) we get value of b as 11.

Hence these numbers are 29 and 11

x - y = 8

x^2 - y^2 = 400

let x = 8 + y

replacing x

(8 + y)^2 - y^2 = 400

expanding bracket

64 + 16y +y^2 - y^2 = 400

64 + 16y = 400

16y = 336

y= 21

replacing y in x = 8 + y

x = 29

The differende of two figures is 8

x - y = 8

The difference of two squares if 400

x² - y² = 400