Question

express 25 square as the sum of two consecutive natural numbers

Answer 1

Answer:

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Step-by-step explanation:

25=4 ka square + 3 ka square

16+9=25

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Answer 2

Answer:

Two consecutive natural numbers are $3$ and $4$.

Step-by-step explanation:

Let two natural consecutive numbers be $x$ and $x+1$.

Then, according to question

⇒ $x^2+(x+1)^2=25$

⇒ $x^2+x^2+2x+1=25$ (Using $(a+b)^2=a^2+2ab+b^2$)

⇒ $2x^2+2x=24$

⇒ $x^2+x=12$

⇒ $x^2+x-12=0$

Using middle term splitting method, solve the quadratic equation as follows:

$x^2+4x-3x-12=0$

$x(x+4)-3(x+4)=0$

$(x+4)(x-3)=0$

⇒ $x=-4$ and $x=3$

$x=-4$ is not possible as natural number cannot be negative.

So, $x=3$ and $x+1 =4$.

Therefore, $25$ can be expressed the sum of the square of two consecutive natural numbers $3$ and $4$.

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