Question

plzzz telll this ques

Answer 1

Its done in a bit short cut method hope this helps

Answer 2

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1. Find a ^ 2 + b ^ 2 when a + b = 9 and ab = 20.

Given,

( a + b ) = 9

Squaring both sides,

( a + b ) ^2 = 9 ^ 2

a ^ 2 + b ^ 2 + 2 ab = 81

a ^ 2 + b ^ 2 + 2 * 20 = 81

a ^ 2 + b ^ 2 + 40 = 81

a^ 2 + b ^ 2 = 81 - 40

a ^ 2 + b ^ 2 = 41.

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2. Find p ^ 2 + q ^ 2 if ( p - q ) = 6 and ( p + q ) = 14.

Solution : ( p - q ) = 6 ------------------------------- equation 1 

                ( p + q ) = 14  ----------------------------------- equation 2

By adding both equations,

p - q + p + q = 6 + 14

2 p = 20 

p = 20 / 2 = 10.

By putting the value of p in equation 1 ,

p - q = 6

10 - q = 6

10 - 6 = q

q = 4.

Now,

=  p ^ 2 + q ^ 2

= ( 10 ) ^ 2 + 4 ^ 2

= 100 + 16

= 116

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3. Find mn if ( m + n ) = 8 and ( m - n ) = 2.

Solution : ( m + n ) = 8  ------------------------------ equation 1

                ( m - n ) = 2  ------------------------------- equation 2

By adding equation 1 and equation 2,

 m + n + m - n = 8 + 2

2 m = 10

m = 10 / 2

m = 5.

By putting the value of m in equation 1 ,

m + n = 8 

5 + n = 8

n = 8 - 5

n = 3

Now,

  = mn = 5 * 3 = 15.