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# The Sum of a Number and Its Square is 63/4. Find the Numbers - CBSE Class 10 - Mathematics

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ConceptSolutions of Quadratic Equations by Factorization

#### Question

The sum of a number and its square is 63/4. Find the numbers.

#### Solution

Let the number be x.

Given that the sum of x and its square = 63/4

⇒ x + 𝑥2 = 63/4

⇒ 4x + 4x2 - 63 = 0

⇒ 4x2 + 4x - 63 = 0

⇒ 4x2 + 4x - 63 = 0 ....................(i)

The value of x can be found by the formula

x=(-b+-sqrt(b^2-4ac))/(2a)

⇒ here a = 4, b = 4 and c = -63 from (i)

x=(-4+-sqrt(16-4xx4xx-63))/(2xx4)

=(-4+-sqrt(16+16xx63))/(2xx4)

x=(-4+-sqrt(16+1008))/8

Therefore,

x=(-4+sqrt(16+1008))/8=7/2

Or

x=(-4-sqrt(16+1008))/8=-9/2

∴ The values of x i. e. , the numbers is 7/2 , -9/2.
.

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#### APPEARS IN

Solution The Sum of a Number and Its Square is 63/4. Find the Numbers Concept: Solutions of Quadratic Equations by Factorization.
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