if a+b=7 and ab=10 then find the value a-b.

solution:-

let x=a-b ..........(1) 

given  a+b=7 and ab=10

from(1)

 x=a-b

x=√ (a-b)²   

=√(a²-2ab+b²)

=√(a²-2ab+b²-2ab-2ab)

=√ (a+b)²  -4ab

put value of a+b and ab 

=√ {(7)²  -4×10}

=√{49-40}

=√9

=3 ans 

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if a+b=7 and ab=10 find the value of a2 +b2

solution:-

let x=a²+ b²

..........(1) 

given  a+b=7 and ab=10

from(1)

 x=a²+ b² 

=(a+b)² -2ab

=(7)² -2х10

=49-20

=29

if a+b=7 and ab=12 find the value of a2 +b2

solution:-

let x=a²+ b²

..........(1) 

given  a+b=7 and ab=10

from(1)

 x=a²+ b² 

=(a+b)² -2ab

=(7)² -2х12

=49-24

=25

 if a+b=7 and ab=11 find the value of (a-b)

solution:-

let x=a-b ..........(1) 

given  a+b=7 and ab=11

from(1)

 x=a-b

x=√ (a-b)²   

=√(a²-2ab+b²)

=√(a²-2ab+b²-2ab-2ab)

=√ (a+b)²  -4ab

put value of a+b and ab 

=√ {(7)²  -4×11}

=√{49-44}

=√5 ans

 if a+b=9 and ab=10 find the value of a-b

solution:-

let x=a-b ..........(1) 

given  a+b=9 and ab=10

from(1)

 x=a-b

x=√ (a-b)²   

=√(a²-2ab+b²)

=√(a²-2ab+b²-2ab-2ab)

=√ (a+b)²  -4ab

put value of a+b and ab 

=√ {(9)²  -4×10}

=√{81-40}

=√41 ans

if a+b=7 and ab=12 find the value of a-b

solution:-

let x=a-b ..........(1) 

given  a+b=7 and ab=12

from(1)

 x=a-b

x=√ (a-b)²   

=√(a²-2ab+b²)

=√(a²-2ab+b²-2ab-2ab)

=√ (a+b)²  -4ab

put value of a+b and ab 

=√ {(7)²  -4×12}

=√{49 -48}

=√1 

if a+b=1 and a-b=7 find ab

 solution:-

Given a+b=1..........(1)

and a-b=7 .........(2)

from (1) and (2)

  a+b=1..........(1)

  a-b=7 .........(2)

after solving 

2a=8

a=8/2

a=4

b=-3

now ab=4×(-3)= -12