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Use the identity (x2+y2)2=(x2−y2)2+(2xy)2 to determine the sum of the squares of two numbers if the difference of the squares of the numbers is 5 and the product of the numbers is 6.

Respuesta :

remotecontrolbrain

let a,b be the two numbers. we know that a2-b2=5 and a*b=6

using the formula we are given

[tex](a^2+b^2)^2 = 5^2 + 12^2 = 169[/tex] we get the solution [tex]\sqrt{169} = 13[/tex]

aachen

Answer:

13

Step-by-step explanation:

Let x and y are two numbers. The difference of the squares if the two numbers is 5 and the product of the numbers is 6 such that,

[tex](x^2-y^2)=5[/tex]......................(1)

[tex]xy=6[/tex]..........(2)

We need to find the sum of the squares of two numbers. By using following identities it can be calculated as :

[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]

Using equation (1) and (2) in above equation, we get :

[tex](x^2+y^2)^2=5^2+(2\times 6)^2[/tex]

[tex]x^2+y^2=\sqrt{5^2+12^2}[/tex]

[tex]x^2+y^2=13[/tex]

So, the sum of squares of two numbers is 13. Hence, this is the required solution.

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