The number of elements in the set { (a, b) : | vedclass

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

Question

(C) The given set is defined by the equation $2a^2 + 3b^2 = 35$,where $a, b \in \mathbb{Z}$.We test integer values for $a$ and $b$:If $a = \pm 2$,then

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) The given set is defined by the equation $2a^2 + 3b^2 = 35$,where $a, b \in \mathbb{Z}$.We test integer values for $a$ and $b$:If $a = \pm 2$,then $2(4) + 3b^2 = 35 \implies 8 + 3b^2 = 35 \implies 3b^2 = 27 \implies b^2 = 9 \implies b = \pm 3$.This gives the pairs: $(2, 3), (2, -3), (-2, 3), (-2, -3)$.If $a = \pm 4$,then $2(16) + 3b^2 = 35 \implies 32 + 3b^2 = 35 \implies 3b^2 = 3 \implies b^2 = 1 \implies b = \pm 1$.This gives the pairs: $(4, 1), (4, -1), (-4, 1), (-4, -1)$.Checking other values of $a$: if $a = 0, 3b^2 = 35$ (no integer solution); if $a = \pm 1, 2 + 3b^2 = 35 \implies 3b^2 = 33 \implies b^2 = 11$ (no integer solution); if $a = \pm 3, 18 + 3b^2 = 35 \implies 3b^2 = 17$ (no integer solution).Thus,the total number of elements is $4 + 4 = 8$.

The number of elements in the set $\{ (a, b) : 2a^2 + 3b^2 = 35, a, b \in \mathbb{Z} \}$,where $\mathbb{Z}$ is the set of all integers,is

Similar Questions

In a certain office,$72 \%$ of the workers prefer cold drink and $44 \%$ prefer tea. If each of them prefers cold drink or tea and $40$ like both,then the total number of workers in the office is

Write down the power set of the set ${0}.$

If $A = \{ 1, 2, 3, 4 \}$ and $B = \{ a, b \}$,and $f$ is a mapping such that $f: A \to B$,then the Cartesian product $A \times B$ is:

In a class of $50$ students,$35$ opted for Mathematics and $37$ opted for Biology. How many have opted for both Mathematics and Biology? How many have opted for only Mathematics? (Assume that each student has to opt for at least one of the subjects).

The domain of the function $f(x) = \log_{3 + x}(x^2 - 1)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module