Question

the product of two number is 20 and the sum of square is 41 find the number.​

Answer 1

Answer:

ANSWER 9

☆APPLY (a+b)² IDENTITY☆

let the 2 numbers be a,b

since a×b= 20

and a²+b² = 41

(a+b)² = a²+b²+2ab

= 41 + 2× 20 [ a²+b² and ab given ]

= 81

(a+b)² = 81 [take square root on both sides]

a+b = 9

Answer 2

Answer:

The numbers will be either 5 and 4 or -5 and -4.

Step-by-step explanation:

Let the two numbers be x and y.

Acc. to question

xy=20 and x²+y² = 41

Using identity (x+y)² = x² + y² + 2xy  

Putting above values in this equation

(x+y)² = 41 + 2×20

(x+y)² = 41 + 40

(x+y)² = 81

x+y = ±9  -eq.1

Now, use the identity (x-y)² = x² + y² - 2xy  

Putting values we get,

(x-y)² = 41 - 2×20

(x-y)² = 41 - 40

(x-y)² = 1

x-y = ±1  -eq.2

Now taking x+y=9 from eq.1 and x-y = 1 from eq.2 we get,

x = 5 and y = 4

Taking x+y= -9 from eq.1 and x-y = -1 from eq.2 we get,

x = -5 and y = -4

So, the numbers will be either 5 and 4 or -5 and -4.