Question

twice the square of a natural number increased by thrice the number is equal to 90. find the number​

Answer 1

Answer:

Step-by-step explanation:

2x^2 + 3x = 90

=> 2x^2 +3x - 90 = 0

=> 2x^2 + (15-12)x - 90 = 0

=> 2x^2 + 15x - 12x -90 = 0

=> x(2x + 15) - 6(2x + 15) = 0

=> (2x + 15) (x - 6) = 0

Therefore : x - 6 = 0

=> x = 6

Since X is a natural number.

I know it's late but hope it helps

Answer 2

The number is 6.

Given:

• Twice the square of a natural number increased by thrice the number is equal to 90.

To find:

• Find the number.

Solution:

Concept to be used:

1. Assume the number.
2. Create equation from the equation.
3. Solve the equation.

Step 1:

Write equation from the statement.

Let the number is x.

Twice the square of number is 2x².

Thrice the number is 3x.

So,

$\bf 2 {x}^{2} + 3x = 90$

Step 2:

Solve the equation.

$2 {x}^{2} + 3x - 90 = 0$

or

split the middle term for factorization.

$2 {x}^{2} + 15x - 12x - 90 = 0$

or

$x(2x + 15) - 6(2x + 15) = 0$

or

$(x - 6)(2x + 15) = 0$

or

$\bf \red{x = 6 }$

or

$x = - 7.5$

Discard this value of x; as number is natural number.

Thus,

The number is 6.

Verification:

$= 2( {6}^{2} ) + 3(6)$

or

$= 2 \times 36 + 18$

or

$= 72 + 18$

or

$= 90$

Hence verified.

#SPJ3

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