Question

Can someone help me with the below question???

Answer 1

so 2a+3b=±13

Explanation:

4a²+9b²=97

ab=6

2a+3b=?

by using formula

(a+b)²=a²+b²+2ab

(2a+3b)²=(2a)²+(3b)²+2(2a)(3b)

(2a+3b)²=4a²+9b²+12ab

putting values

(2a+3b)²=97+12(6)

(2a+3b)²=97+72

(2a+3b)²=169

taking square root on both sides

√(2a+3b)²=√169

2a+3b=±13

i hope it will help you

Answer 2

2a+3b = 13

Explanation:

Using this formula

`(x+y)^2 = x^2+y^2+2xy`

Where,

x = 2a and y = 3b

Putting in the above formula

=>
`(2a+3b)^2=4a^2+9b^2+12ab`

Putting 4a²+9b² = 97 and ab = 6

=> (2a+3b)² = 97+12(6)

=> (2a+3b)² = 97+72

=> (2a+3b)² = 169

Taking sqrt on both sides

=> 2a+3b = 13