Question

Find a and b
$\bf \: a + b = 17$
$\bf \: {a}^{2} + {b}^{2} = 157$
​

Answer 1

Answer:-

• a = 16
• b = 11

step-by-step solution:-

GIVEN:-

• a + b = 27 ________ {1}
• a² + b² = 157

To Find:

• Value of a and b

Using Identity:

• ( a + b )² = a² + b² + 2ab
• ( a - b )² = a² + b² - 2ab

SOLUTION:

Firstly we will find the value of ab.

⇒ ( a + b )² = a² + b² + 2ab

Putting the values which are given

⇒ ( 17 )² = 157 + 2ab

⇒ 289 = 157 + 2ab

⇒ 289 - 157 = 2ab

⇒ 2ab = 132

⇒ ab = 132/2

⇒ ab = 66

Now putting the given values in identity

⇒ ( a - b )² = a² + b² - 2ab

⇒ ( a - b )² = 157 - 2 × 66

⇒ ( a - b )² = 157 - 132

⇒ ( a - b )² = 25

⇒ a - b = √25

⇒ a - b = 5______{2}

Adding {1} and {2}

⇒ a + b + a - b = 27 + 5

⇒ 2a = 32

⇒ a = 32/2

⇒ a = 16

Putting the value of a in {2},

⇒ a - b = 5

⇒ 16 - b = 5

⇒ b = 16 - 5

⇒ b = 11

⚘ Hence, the value of a and b are 16 and 11 respectively.

━━━━━━━━━━━━━━━━━━