Question

if 2a+3b=14 and 2a-3b=2. find the value of ab.

Answer 1

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here is your answer ,

so, let's check this out :-

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here we go now :-

2a+3b = 14 ------------ (i)

2a-3b = 2-------------;---(ii)

adding (i) and (ii), we get

4a = 16

a = 4

now ,

putting a in (i) ,, we get .

2a + 3b = 14

8+ 3b = 14

3b = 6

b = 2

now,

as your question says :-

find value of ab ,

putting value of a = 4 and b = 2 , we get ,

ab = 4×2 = 8

hence , value of ab = 8 ,

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Answer 2

Heya!!

Thanks for asking the question

Answer :

Explanation :

Given,

2a + 3b = 14

2a - 3b = 2

let 2a be x and 3b be y

Therefore,

2a + 3b be x + y

and 2a - 3b be x - y

xy = 6ab

Now squaring both of these, we get -

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

Substituting the values we get : -

$196 = {x}^{2} + {y}^{2} + 2xy \: \: \: (i)$

${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy$

Substituting the values, we get-

$4 = {x }^{2} + {y}^{2} - 2xy \: \: \: \: \: \: (ii)$

Now, adding (i) and ( ii ) , we get -

$200 = 2( {x}^{2} + {y }^{2} )$
From this,

${x}^{2} + {y}^{2} = 100$

Now putting the value of x^2 + y^2 in ( ii )

$100 - 2xy = 4$
Now solving for xy using transposition.

$- 2xy = - 96$

$xy = 48$

Since, xy = 6ab

ab = 8 . ( Answer )

Hope it helps you : )