Divide 29 into two parts such that the sum of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the two parts be $x$ and $(29 - x)$.According to the problem,the sum of their squares is $425$:$x^2 + (29 - x)^2 = 425$$x^2 + (841 - 58x + x^2

Vedclass · Accepted Answer

$13, 16$

Vedclass · Answer

(A) Let the two parts be $x$ and $(29 - x)$.According to the problem,the sum of their squares is $425$:$x^2 + (29 - x)^2 = 425$$x^2 + (841 - 58x + x^2) = 425$$2x^2 - 58x + 841 - 425 = 0$$2x^2 - 58x + 416 = 0$Dividing by $2$:$x^2 - 29x + 208 = 0$Factoring the quadratic equation:$x^2 - 13x - 16x + 208 = 0$$x(x - 13) - 16(x - 13) = 0$$(x - 13)(x - 16) = 0$So,$x = 13$ or $x = 16$.If $x = 13$,the other part is $29 - 13 = 16$.If $x = 16$,the other part is $29 - 16 = 13$.Thus,the two parts are $13$ and $16$.

Divide $29$ into two parts such that the sum of their squares is $425$.

Similar Questions

Find the roots of the quadratic equation by using the quadratic formula:
$\frac{1}{2} x^{2}-\sqrt{11} x+1=0$

Examine whether the following equation is quadratic or not: $3x^{2} + 5\sqrt{x} + 3 = 0$.

If the radius of a sphere is doubled,its volume becomes $\ldots \ldots \ldots \ldots$ times the original volume.

Obtain the roots of the following quadratic equation by using the quadratic formula: $p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0$

State whether the quadratic equation $(x+1)(x-2)+x=0$ has two distinct real roots. Justify your answer.

Vedclass Test Series

Exam Paper Generator

Online Exam Module