Question

sum of two numbers is 34 and addition of square of both numbers is 650. Find the smallest number​

Answer 1

Answer:

1st no. + 2nd no. = 34.

square of 1st no. + square of 2nd no. = 650.

To find:-

The smallest no.

Solution:-

Let the 1st no. be x and the 2nd no. y .

So, According to the question

x + y = 34______ eq 1.

x² + y² = 650______ eq 2.

now squaring both side of eq 1.

( x+ y )² = 34²

x² + y² + 2xy = 1156.

650 + 2xy = 1156

2xy = 1156 - 650

2xy = 506

( x - y )² = x² + y² - 2xy

= 650 - ( 506 )

= 144

= root 0f 144

x- y = 12._____eq 3

So adding eq 1 and 3

x + y + x - y = 34 + 12

2x = 46

x = 46/2

x = 23.

and y = x - 12

= 23 - 12

= 11

Therefore the smallest no. is 11

I hope this concept is clear

Answer 2

Given:

a + b = 34........(i)

a² + b² = 650.........(ii)

Now, According to Question

➟ (a + b)² = (34)²

➟ a² + b² + 2ab = 1156

Use the value of eq(ii)

➟ a² + b² + 2ab = 1156

➟ 650 + 2ab = 1156

➟ 2ab = 1156 - 650

➟ 2ab = 506---------(iii)

Now, subtract (iii) from (ii)

➟ (a² + b²) - (2ab) = (650) - (506)

➟ a² + b² - 2ab = 650 - 506

➟ (a - b)² = 144

On removing square

➟ a - b = √144

➟ a - b = 12-------------(iv)

On solving (i) & ((iv)

➟ (a + b) - (a - b) = 34 - 12

➟ a + b - a + b = 22

➟ 2b = 22

➟ b = 22/2

➟ b = 11

And

➟ a - b = 12

➟ a - 11 = 12

➟ a = 12 + 11

➟ a = 23

Therefore:-

The smallest number is 11.