Question

The difference of the squares of two
numbers is 135 and their difference is 5
the product of the numbers is​

Answer 1

Answer:

$\huge\boxed{\fcolorbox{lime}{Pink}{HEYA YOUR ANSWER IS HERE⚡}}$

Step-by-step explanation:

a + b + c = 10

⇒ (a + b + c)2 = (10)2

⇒ a2 + b2 + c2 + 2ab + 2bc + 2ca = 100

⇒ 38 + 2(ab + bc + ca) = 100

⇒ 2(ab + bc + ca) = 62

⇒ 2(ab + bc + ca) = 62

⇒ (ab + bc + ca) = 62/2

⇒ ab + bc + ca = 31

Alternative Method

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca

⇒ (10)2 = 38 + 2(ab + bc + ca)

⇒ 100 = 38 + 2(ab + bc + ca)

⇒ 100 - 38 + 2(ab + bc + ca)

⇒ 62 = 2(ab + bc + ca)

⇒ 62/2 = ab + bc + ca

⇒ 31 = ab + bc + ca

HEYA FRIEND HAVE A GOOD DAY

∴ ab + bc + ca = 31

Answer 2

Answer:

176

Step-by-step explanation:

We will let one number = x and the other =y

From the information we can derive these equations

$x {}^{2} + y {}^{2} = 135$

$x - y = 5$

We use simultaneous equations to find y

$x = 5 + y$

${(5 + y)}^{2} - y {}^{2} = 135$

$25 + 10y = 135$

$y = 11$

We use the y value to find x

$x - 11 = 5$

$x = 16$

If we substitute these values into original equation we find they are correct

Therefore the product is 11*16=176