Question

If a-b=7,a³-b³=133 then find i)ab ii)a²+b²​

Answer 1

Answer:

is given that,

a−b=7

let us cube on both sides, we get

(a−b)

3

=(7)

3

a

3

+b

3

−3ab(a−b)=343

133−3ab×7=343

133−21ab=343

−21ab=343−133

21ab=210

ab=−210/21

ab=−10

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given:-

a-b = 7 and a^3-b^3=133

To find:-

Find the following values

i)ab ii)a²+b²

Solution:-

Given that

a-b=7

a^3-b^3=133

we know that

(a-b)^3=a^3-b^3-3ab(a-b)

=>7^3=133-3ab(7)

=>343=133-21ab

=>343-133=-21ab

=>210=-21ab

=>-21 ab=210

=>ab=210/-21

=>ab=-10

I)ab=-10

now we know that

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

=>7^2=a^2+b^2-2(-10)

=>49=a^2+b^2+20

=>a^2+b^2=49-20

(ii)a^2+b^2=29

Answer:-

The value of ab= -10

The value of a^2+b^2=29

Used formulae:-

• (a-b)^3=a^3-b^3-3ab(a-b)
• (a-b)^2 =a^2+b^2-2ab