Question

Divide 29 into two parts so that the sum of the squares of the parts is 425

Answer 1

Step-by-step explanation:

Let the two parts be x and y

x + y = 29 ⇒ y = 29 - x

so according to question x² + y² = 425

⇒ x² + (29 - x)² = 425

⇒ x² + 841 + x² - 58x = 425

⇒2x² - 58x + 416 = 0

⇒ x² - 29x + 208 = 0

⇒ x² - 13x - 16x + 208 = 0

⇒ x(x - 13) - 16(x - 13) = 0

⇒ (x - 16)(x - 13) = 0

so x = 16 or 13

Answer 2

Let one of the part be ' x ',

Then,

the other part will be ' 29-x '

ACCORDING TO THE QUESTION:-

${x}^{2} + {29-x}^{2} = {425}$

${x}^{2} + {841} + {x}{2} - {58x} = {425}$

${2x}^{2} + {841} - {425} - {58x} = {0}$

${2x}^{2} - {58x} + {416} = {0}$

${x}^{2} - {29x} + {208} = {0}$

${x}^{2} - {13x} - {16x} + {208} = {0}$

${x}{(x-13)} - {16}{(x-13)} = {0}$

${(x-16)}{(x-13)} = {0}$

ANSWER:-

${x} = {16}$ or ${x} = {13}$

${29} - {x} = {13}$ or ${29} - {x} = {16}$