Question

if a+b=6,a-b= 4 then a^2+b^2=?​

Answer 1

Answer:

if a+b=6,a-b= 4 then a^2+b^2=?26

Step-by-step explanation:

Method 1: Squaring & adding the given equations a+b=6a+b=6 & a−b=4a−b=4 , one should get

(a+b)2+(a−b)2=62+42(a+b)2+(a−b)2=62+42

a2+b2+2ab+a2+b2−2ab=36+16a2+b2+2ab+a2+b2−2ab=36+16

2(a2+b2)=522(a2+b2)=52

a2+b2=522=26a2+b2=522=26

Method 2: Adding the given equations: a+b=6a+b=6 & a−b=4a−b=4⟹a+b+a−b=6+4⟹a=5⟹a+b+a−b=6+4⟹a=5

Now, subtracting given equations: a+b−a+b=6−4⟹b=1a+b−a+b=6−4⟹b=1

∴a2+b2=52+12=25+1=26

Answer 2

Answer:

26

Step-by-step explanation:

a+b=6

a=6-b

a-b=4

(6-b)-b=4

6-2b=4

-2b=4-6

2b=2

b=1

a=6-b

a=5

a^2+b^2

5²+1²

25+1

_26_