The sum of 2 positive integers is 151. The lesser number is 19 more than the square root of the greater number, What is the value of the?

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The sum of 2 positive integers is 151. The lesser number is 19 more than the square root of the greater number, What is the value of the greater number minus the lesser number?

Abbie Toy · Accepted Answer

x² + x + 19 = 151 x² + x – 132 = 0x = 11 (valid) or -12 (invalid, as per the question)The smaller number is 11+19 = 30 and the greater number is 121.

Abbie Toy · Answer

y = 151 – x y = x^(1/2) + 19151 – x = x^(1/2) + 19 x^(1/2) = 132 – xx = x^2 – 264x + 132^2x^2 – 265x + 17424 = 0(x – 144)(x – 121) = 0Solutions:x = 144, y = 7x = 121, y = 30The numbers are 144 and 7 or 121 and 30The value of the greater number minus the lesser number is either 137 or 91.

Abbie Toy · Answer

A great way to start word problems is to write down everything that is in words in the problem in mathematical terms– The sum of 2 positive integers is 151(eq1)a + b = 151– The lesser number is 19 more than the square root of the greater number(eq2)a – 19 = squareroot(b)now you can just plug in. Let’s set equation 2 to b= (I tried a= and it was pretty complicated)b = (a-19)(a-19)b = a^2 -38a + 361 and plug that into equation 1a + (a^2 -38a + 361) = 151set that equation = zero so that we can use the quadratic formulaa^2 – 37a + 210 = 0I leave the quadratic formula to you. Remember that both a and b must be positive, so you should use the positive value, and not the negative value, that you get from the quadratic formula.Just plug the value of a into equation 1 to get the value of b.

Abbie Toy · Answer

a + b^2 = 151a = b + 19b + 19 + b^2 = 151b^2 + b – 132 = 0 b = (-1 +/- sqrt(1 + 528)) / 2b = (-1 +/- sqrt(529)) / 2b = (-1 +/- 23) / 2b = -24/2 , 22/2b = -12 , 11a and b > 0b = 11b^2 = 121a = 3030 and 121 are your numbers

Abbie Toy · Answer

You have x+y = 115and x = 19 + √y or x – 19 = √y.Therefore x^2 – 38x + 281 = y – 115 – xSolve the quadratic for x.

Abbie Toy · Answer

91

Brandyn Moore PhD

The sum of 2 positive integers is 151. The lesser number is 19 more than the square root of the greater number, What is the value of the?

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