Question

plzzzz give me the ans of this question

Answer 1

1. a²+4b²=41

1. ab=10

1. now, (a+2b)²=a²+4b²+4ab

1. =41+40=81

1. so,a+2b=9

1. and,(a-2b)²=a²+4b²-4ab

1. so,a-2b= 1

Answer 2

Given

a^2 + 4b^2 = 41

ab = 10

we know that

(a + b)^2 = a^2 + b^2 +2ab

here a = a , b= 2b

so..

(a + 2b)^2

= a^2 + (2b)^2 + 2(a)(2b)

=a^2 + 4b^2 + 4ab

substitute given values...

= 41 + 4(10) = 81

(a+ 2b)^2 = 81

(a + 2b) = √81 = 9.....

Similarly We know that...

(a-b)^2 = a^2 +b^2 - 2ab or ( a+b)^2 - 4ab

here a = a , b = 2b

(a - 2b)^2 = (a^2 + (2b)^2 -2.a.2b) = a^2 + 4b^2 - 4ab

substitute given values...

= 41 - 4(10)

= 41 - 40

= 1

so (a-2b)^2 = 1..

(a-2b) = √1 = 1....

so

a + 2b = 9

a - 2b = 1........