Question

√x+√y=√a what is is the for answer


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Answer 1

Answer:

(1) (√x) + y = 7

(2) x + √y = 11

I did this:

Let u = √x and v = √y

So (1) and (2) can be re-written as:

(1') u + v2 = 7

(2') u2 + v = 11

(1') —> u = 7-v2

Substituting into (2') for u:

(7-v2)2 + v = 11

(49 - 14v2 + v4) + v = 11

v4 - 14v2 + v + 38 = 0

(v-2)(v3+2v2-10v-19) = 0

(v-2)(v-3.13131)(v+1.84813)(v+3.28319) = 0

So possible answers are:

v=2 —> y=4 —(from (1))—> √x=3 —> x=9

v=3.13131 —> y=9.80510 ——> √x=-2.8051 —> x=7.86859

v=-1.84813 —> y=3.41558 ——> √x=3.58442 —> x=12.84807

v=-3.28319 —> y=10.77934 ——> √x=-3.77934 —> x=14.28341

Check:

x=9, y=4:

(1) 3+4=7 (ok)

(2) 9+2=11 (ok)

x=7.86859, y=9.80510

(1) -2.8051+9.80510=7 (ok) (only if we take the negative root of x)

(2) 7.86859+3.13131=11 (ok)

x=12.84807, y=3.41558

(1) 3.58442+3.41558=7 (ok)

(2) 12.84807-1.84813=11 (ok) (only if we take the negative root of y)

x=14.28341, y=10.77934

(1) -3.77934+10.77934=7 (ok) (only if we take the negative root of x)

(2) 14.28341-3.28319=11 (ok) (only if we take the negative root of y)

Given no other information, √a is defined to be the positive square root of a only —> so only x=9, y=4 is a proper answer.