Question

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

Please don't answer if you don't know so Correct Solutions only ​

Answer 1

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.

Answer 2

Given:-

• 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.

┏─━─━─━∞◆∞━─━─━─┓

✭✮ӇЄƦЄ ƖƧ ƳƠƲƦ ƛƝƧƜЄƦ✮✭

┗─━─━─━∞◆∞━─━─━─┛

${\huge{\mathtt{\red{Thank\:You}}}}$